Trigonometric functions

From Rosetta Code
Task
Trigonometric functions
You are encouraged to solve this task according to the task description, using any language you may know.
Task

If your language has a library or built-in functions for trigonometry, show examples of:

  •   sine
  •   cosine
  •   tangent
  •   inverses   (of the above)


using the same angle in radians and degrees.

For the non-inverse functions,   each radian/degree pair should use arguments that evaluate to the same angle   (that is, it's not necessary to use the same angle for all three regular functions as long as the two sine calls use the same angle).

For the inverse functions,   use the same number and convert its answer to radians and degrees.

If your language does not have trigonometric functions available or only has some available,   write functions to calculate the functions based on any   known approximation or identity.

ACL2[edit]

This example is incomplete. Please ensure that it meets all task requirements and remove this message.

(This doesn't have the inverse functions; the Taylor series for those take too long to converge.)

(defun fac (n)
(if (zp n)
1
(* n (fac (1- n)))))
 
(defconst *pi-approx*
(/ 3141592653589793238462643383279
(expt 10 30)))
 
(include-book "arithmetic-3/floor-mod/floor-mod" :dir :system)
 
(defun dgt-to-str (d)
(case d
(1 "1") (2 "2") (3 "3") (4 "4") (5 "5")
(6 "6") (7 "7") (8 "8") (9 "9") (0 "0")))
 
(defmacro cat (&rest args)
`(concatenate 'string ,@args))
 
(defun num-to-str-r (n)
(if (zp n)
""
(cat (num-to-str-r (floor n 10))
(dgt-to-str (mod n 10)))))
 
(defun num-to-str (n)
(cond ((= n 0) "0")
((< n 0) (cat "-" (num-to-str-r (- n))))
(t (num-to-str-r n))))
 
(defun pad-with-zeros (places str lngth)
(declare (xargs :measure (nfix (- places lngth))))
(if (zp (- places lngth))
str
(pad-with-zeros places (cat "0" str) (1+ lngth))))
 
(defun as-decimal-str (r places)
(let ((before (floor r 1))
(after (floor (* (expt 10 places) (mod r 1)) 1)))
(cat (num-to-str before)
"."
(let ((afterstr (num-to-str after)))
(pad-with-zeros places afterstr
(length afterstr))))))
 
(defun taylor-sine (theta terms term)
(declare (xargs :measure (nfix (- terms term))))
(if (zp (- terms term))
0
(+ (/ (*(expt -1 term) (expt theta (1+ (* 2 term))))
(fac (1+ (* 2 term))))
(taylor-sine theta terms (1+ term)))))
 
(defun sine (theta)
(taylor-sine (mod theta (* 2 *pi-approx*))
20 0)) ; About 30 places of accuracy
 
(defun cosine (theta)
(sine (+ theta (/ *pi-approx* 2))))
 
(defun tangent (theta)
(/ (sine theta) (cosine theta)))
 
(defun rad->deg (rad)
(* 180 (/ rad *pi-approx*)))
 
(defun deg->rad (deg)
(* *pi-approx* (/ deg 180)))
 
(defun trig-demo ()
(progn$ (cw "sine of pi / 4 radians: ")
(cw (as-decimal-str (sine (/ *pi-approx* 4)) 20))
(cw "~%sine of 45 degrees: ")
(cw (as-decimal-str (sine (deg->rad 45)) 20))
(cw "~%cosine of pi / 4 radians: ")
(cw (as-decimal-str (cosine (/ *pi-approx* 4)) 20))
(cw "~%tangent of pi / 4 radians: ")
(cw (as-decimal-str (tangent (/ *pi-approx* 4)) 20))
(cw "~%")))
sine of pi / 4 radians:    0.70710678118654752440
sine of 45 degrees:        0.70710678118654752440
cosine of pi / 4 radians:  0.70710678118654752440
tangent of pi / 4 radians: 0.99999999999999999999

ActionScript[edit]

Actionscript supports basic trigonometric and inverse trigonometric functions via the Math class, including the atan2 function, but not the hyperbolic functions.

trace("Radians:");
trace("sin(Pi/4) = ", Math.sin(Math.PI/4));
trace("cos(Pi/4) = ", Math.cos(Math.PI/4));
trace("tan(Pi/4) = ", Math.tan(Math.PI/4));
trace("arcsin(0.5) = ", Math.asin(0.5));
trace("arccos(0.5) = ", Math.acos(0.5));
trace("arctan(0.5) = ", Math.atan(0.5));
trace("arctan2(-1,-2) = ", Math.atan2(-1,-2));
trace("\nDegrees")
trace("sin(45) = ", Math.sin(45 * Math.PI/180));
trace("cos(45) = ", Math.cos(45 * Math.PI/180));
trace("tan(45) = ", Math.tan(45 * Math.PI/180));
trace("arcsin(0.5) = ", Math.asin(0.5)*180/Math.PI);
trace("arccos(0.5) = ", Math.acos(0.5)*180/Math.PI);
trace("arctan(0.5) = ", Math.atan(0.5)*180/Math.PI);
trace("arctan2(-1,-2) = ", Math.atan2(-1,-2)*180/Math.PI);
 

Ada[edit]

Ada provides library trig functions which default to radians along with corresponding library functions for which the cycle can be specified.
The examples below specify the cycle for degrees and for radians.
The output of the inverse trig functions is in units of the specified cycle (degrees or radians).

with Ada.Numerics.Elementary_Functions;
use Ada.Numerics.Elementary_Functions;
with Ada.Float_Text_Io; use Ada.Float_Text_Io;
with Ada.Text_IO; use Ada.Text_IO;
 
procedure Trig is
Degrees_Cycle : constant Float := 360.0;
Radians_Cycle : constant Float := 2.0 * Ada.Numerics.Pi;
Angle_Degrees : constant Float := 45.0;
Angle_Radians : constant Float := Ada.Numerics.Pi / 4.0;
procedure Put (V1, V2 : Float) is
begin
Put (V1, Aft => 5, Exp => 0);
Put (" ");
Put (V2, Aft => 5, Exp => 0);
New_Line;
end Put;
begin
Put (Sin (Angle_Degrees, Degrees_Cycle),
Sin (Angle_Radians, Radians_Cycle));
Put (Cos (Angle_Degrees, Degrees_Cycle),
Cos (Angle_Radians, Radians_Cycle));
Put (Tan (Angle_Degrees, Degrees_Cycle),
Tan (Angle_Radians, Radians_Cycle));
Put (Cot (Angle_Degrees, Degrees_Cycle),
Cot (Angle_Radians, Radians_Cycle));
Put (ArcSin (Sin (Angle_Degrees, Degrees_Cycle), Degrees_Cycle),
ArcSin (Sin (Angle_Radians, Radians_Cycle), Radians_Cycle));
Put (Arccos (Cos (Angle_Degrees, Degrees_Cycle), Degrees_Cycle),
Arccos (Cos (Angle_Radians, Radians_Cycle), Radians_Cycle));
Put (Arctan (Y => Tan (Angle_Degrees, Degrees_Cycle)),
Arctan (Y => Tan (Angle_Radians, Radians_Cycle)));
Put (Arccot (X => Cot (Angle_Degrees, Degrees_Cycle)),
Arccot (X => Cot (Angle_Degrees, Degrees_Cycle)));
end Trig;
Output:
 0.70711  0.70711
 0.70711  0.70711
 1.00000  1.00000
 1.00000  1.00000
45.00000  0.78540
45.00000  0.78540
45.00000  0.78540
45.00000  0.78540

ALGOL 68[edit]

Translation of: C
Works with: ALGOL 68 version Standard - no extensions to language used
Works with: ALGOL 68G version Any - tested with release mk15-0.8b.fc9.i386
Works with: ELLA ALGOL 68 version Any (with appropriate job cards) - tested with release 1.8.8d.fc9.i386
main:(
REAL pi = 4 * arc tan(1);
# Pi / 4 is 45 degrees. All answers should be the same. #
REAL radians = pi / 4;
REAL degrees = 45.0;
REAL temp;
# sine #
print((sin(radians), " ", sin(degrees * pi / 180), new line));
# cosine #
print((cos(radians), " ", cos(degrees * pi / 180), new line));
# tangent #
print((tan(radians), " ", tan(degrees * pi / 180), new line));
# arcsine #
temp := arc sin(sin(radians));
print((temp, " ", temp * 180 / pi, new line));
# arccosine #
temp := arc cos(cos(radians));
print((temp, " ", temp * 180 / pi, new line));
# arctangent #
temp := arc tan(tan(radians));
print((temp, " ", temp * 180 / pi, new line))
)
Output:
+.707106781186548e +0  +.707106781186548e +0
+.707106781186548e +0  +.707106781186548e +0
+.100000000000000e +1  +.100000000000000e +1
+.785398163397448e +0  +.450000000000000e +2
+.785398163397448e +0  +.450000000000000e +2
+.785398163397448e +0  +.450000000000000e +2

ALGOL W[edit]

begin
 % Algol W only supplies sin, cos and arctan as standard. We can define  %
 % arcsin, arccos and tan functions using these. The standard functions  %
 % use radians so we also provide versions that use degrees  %
 
 % convert degrees to radians  %
real procedure toRadians( real value x ) ; pi * ( x / 180 );
 % convert radians to degrees  %
real procedure toDegrees( real value x ) ; 180 * ( x / pi );
 % tan of an angle in radians  %
real procedure tan( real value x ) ; sin( x ) / cos( x );
 % arcsin in radians  %
real procedure arcsin( real value x ) ; arctan( x / sqrt( 1 - ( x * x ) ) );
 % arccos in radians  %
real procedure arccos( real value x ) ; arctan( sqrt( 1 - ( x * x ) ) / x );
 % sin of an angle in degrees  %
real procedure sinD( real value x ) ; sin( toRadians( x ) );
 % cos of an angle in degrees  %
real procedure cosD( real value x ) ; cos( toRadians( x ) );
 % tan of an angle in degrees  %
real procedure tanD( real value x ) ; tan( toRadians( x ) );
 % arctan in degrees  %
real procedure arctanD( real value x ) ; toDegrees( arctan( x ) );
 % arcsin in degrees  %
real procedure arcsinD( real value x ) ; toDegrees( arcsin( x ) );
 % arccos in degrees  %
real procedure arccosD( real value x ) ; toDegrees( arccos( x ) );
 
 
 % test the procedures %
begin
 
real piOver4, piOver3, oneOverRoot2, root3Over2;
piOver3 := pi / 3; piOver4  := pi / 4;
oneOverRoot2 := 1.0 / sqrt( 2 ); root3Over2 := sqrt( 3 ) / 2;
 
 
r_w := 12; r_d := 5; r_format := "A"; s_w := 0; % set output format  %
 
write( "PI/4: ", piOver4, " 1/root(2): ", oneOverRoot2 );
write();
write( "sin 45 degrees: ", sinD( 45 ), " sin pi/4 radians: ", sin( piOver4 ) );
write( "cos 45 degrees: ", cosD( 45 ), " cos pi/4 radians: ", cos( piOver4 ) );
write( "tan 45 degrees: ", tanD( 45 ), " tan pi/4 radians: ", tan( piOver4 ) );
write();
write( "arcsin( sin( pi/4 radians ) ): ", arcsin( sin( piOver4 ) ) );
write( "arccos( cos( pi/4 radians ) ): ", arccos( cos( piOver4 ) ) );
write( "arctan( tan( pi/4 radians ) ): ", arctan( tan( piOver4 ) ) );
write();
write( "PI/3: ", piOver4, " root(3)/2: ", root3Over2 );
write();
write( "sin 60 degrees: ", sinD( 60 ), " sin pi/3 radians: ", sin( piOver3 ) );
write( "cos 60 degrees: ", cosD( 60 ), " cos pi/3 radians: ", cos( piOver3 ) );
write( "tan 60 degrees: ", tanD( 60 ), " tan pi/3 radians: ", tan( piOver3 ) );
write();
write( "arcsin( sin( 60 degrees ) ): ", arcsinD( sinD( 60 ) ) );
write( "arccos( cos( 60 degrees ) ): ", arccosD( cosD( 60 ) ) );
write( "arctan( tan( 60 degrees ) ): ", arctanD( tanD( 60 ) ) );
 
end
 
end.
Output:
PI/4:      0.78539 1/root(2):      0.70710

sin 45 degrees:      0.70710 sin pi/4 radians:      0.70710
cos 45 degrees:      0.70710 cos pi/4 radians:      0.70710
tan 45 degrees:      1.00000 tan pi/4 radians:      1.00000

arcsin( sin( pi/4 radians ) ):      0.78539
arccos( cos( pi/4 radians ) ):      0.78539
arctan( tan( pi/4 radians ) ):      0.78539

PI/3:      0.78539 root(3)/2:      0.86602

sin 60 degrees:      0.86602 sin pi/3 radians:      0.86602
cos 60 degrees:      0.50000 cos pi/3 radians:      0.50000
tan 60 degrees:      1.73205 tan pi/3 radians:      1.73205

arcsin( sin( 60 degrees ) ):     60.00000
arccos( cos( 60 degrees ) ):     60.00000
arctan( tan( 60 degrees ) ):     60.00000

AutoHotkey[edit]

Translation of: C
pi := 4 * atan(1) 
radians := pi / 4
degrees := 45.0
result .= "`n" . sin(radians) . " " . sin(degrees * pi / 180)
result .= "`n" . cos(radians) . " " . cos(degrees * pi / 180)
result .= "`n" . tan(radians) . " " . tan(degrees * pi / 180)
 
temp := asin(sin(radians))
result .= "`n" . temp . " " . temp * 180 / pi
 
temp := acos(cos(radians))
result .= "`n" . temp . " " . temp * 180 / pi
 
temp := atan(tan(radians))
result .= "`n" . temp . " " . temp * 180 / pi
 
msgbox % result
/* output
---------------------------
trig.ahk
---------------------------
0.707107 0.707107
0.707107 0.707107
1.000000 1.000000
0.785398 45.000000
0.785398 45.000000
0.785398 45.000000
*/

AWK[edit]

Awk only provides sin(), cos() and atan2(), the three bare necessities for trigonometry. They all use radians. To calculate the other functions, we use these three trigonometric identities:

tangent arcsine arccosine

With the magic of atan2(), arcsine of y is just atan2(y, sqrt(1 - y * y)), and arccosine of x is just atan2(sqrt(1 - x * x), x). This magic handles the angles arcsin(-1), arcsin 1 and arccos 0 that have no tangent. This magic also picks the angle in the correct range, so arccos(-1/2) is 2*pi/3 and not some wrong answer like -pi/3 (though tan(2*pi/3) = tan(-pi/3) = -sqrt(3).)

atan2(y, x) actually computes the angle of the point (x, y), in the range [-pi, pi]. When x > 0, this angle is the principle arctangent of y/x, in the range (-pi/2, pi/2). The calculations for arcsine and arccosine use points on the unit circle at x2 + y2 = 1. To calculate arcsine in the range [-pi/2, pi/2], we take the angle of points on the half-circle x = sqrt(1 - y2). To calculate arccosine in the range [0, pi], we take the angle of points on the half-circle y = sqrt(1 - x2).

# tan(x) = tangent of x
function tan(x) {
return sin(x) / cos(x)
}
 
# asin(y) = arcsine of y, domain [-1, 1], range [-pi/2, pi/2]
function asin(y) {
return atan2(y, sqrt(1 - y * y))
}
 
# acos(x) = arccosine of x, domain [-1, 1], range [0, pi]
function acos(x) {
return atan2(sqrt(1 - x * x), x)
}
 
# atan(y) = arctangent of y, range (-pi/2, pi/2)
function atan(y) {
return atan2(y, 1)
}
 
BEGIN {
pi = atan2(0, -1)
degrees = pi / 180
 
print "Using radians:"
print " sin(-pi / 6) =", sin(-pi / 6)
print " cos(3 * pi / 4) =", cos(3 * pi / 4)
print " tan(pi / 3) =", tan(pi / 3)
print " asin(-1 / 2) =", asin(-1 / 2)
print " acos(-sqrt(2) / 2) =", acos(-sqrt(2) / 2)
print " atan(sqrt(3)) =", atan(sqrt(3))
 
print "Using degrees:"
print " sin(-30) =", sin(-30 * degrees)
print " cos(135) =", cos(135 * degrees)
print " tan(60) =", tan(60 * degrees)
print " asin(-1 / 2) =", asin(-1 / 2) / degrees
print " acos(-sqrt(2) / 2) =", acos(-sqrt(2) / 2) / degrees
print " atan(sqrt(3)) =", atan(sqrt(3)) / degrees
}
Output:
Using radians:
  sin(-pi / 6) = -0.5
  cos(3 * pi / 4) = -0.707107
  tan(pi / 3) = 1.73205
  asin(-1 / 2) = -0.523599
  acos(-sqrt(2) / 2) = 2.35619
  atan(sqrt(3)) = 1.0472
Using degrees:
  sin(-30) = -0.5
  cos(135) = -0.707107
  tan(60) = 1.73205
  asin(-1 / 2) = -30
  acos(-sqrt(2) / 2) = 135
  atan(sqrt(3)) = 60

Axe[edit]

Axe implements sine, cosine, and inverse tangent natively. One period is [0, 256) and the results are [-127, 127] for maximum precision.

The inverse tangent takes dX and dY parameters, rather than a single argument. This is because it is most often used to calculate angles.

Disp sin(43)▶Dec,i
Disp cos(43)▶Dec,i
Disp tan⁻¹(10,10)▶Dec,i
Output:
  113
   68
   32

Below is the worked out math.

On a period of 256, an argument of 43 is equivalent to .

Furthermore, and .

So and . Axe uses approximations to calculate the trigonometric functions.

dX and dY values of 10 mean that the angle between them should be . Indeed, the result .

BaCon[edit]

' Trigonometric functions in BaCon use Radians for input values
' The RAD() function converts from degrees to radians
 
FOR v$ IN "0, 10, 45, 90, 190.5"
d = VAL(v$) * 1.0
r = RAD(d) * 1.0
 
PRINT "Sine: ", d, " degrees (or ", r, " radians) is ", SIN(r)
PRINT "Cosine: ", d, " degrees (or ", r, " radians) is ", COS(r)
PRINT "Tangent: ", d, " degrees (or ", r, " radians) is ", TAN(r)
PRINT
PRINT "Arc Sine: ", SIN(r), " is ", DEG(ASIN(SIN(r))), " degrees (or ", ASIN(SIN(r)), " radians)"
PRINT "Arc CoSine: ", COS(r), " is ", DEG(ACOS(COS(r))), " degrees (or ", ACOS(COS(r)), " radians)"
PRINT "Arc Tangent: ", TAN(r), " is ", DEG(ATN(TAN(r))), " degrees (or ", ATN(TAN(r)), " radians)"
PRINT
NEXT
Output:
prompt$ bacon -q trigonometric-functions.bac 
...
Done, program 'trigonometric-functions' ready.

prompt$ ./trigonometric-functions            
Sine: 0 degrees (or 0 radians) is 0
Cosine: 0 degrees (or 0 radians) is 1
Tangent: 0 degrees (or 0 radians) is 0

Arc Sine: 0 is 0 degrees (or 0 radians)
Arc CoSine: 1 is 0 degrees (or 0 radians)
Arc Tangent: 0 is 0 degrees (or 0 radians)

Sine: 10 degrees (or 0.174533 radians) is 0.173648
Cosine: 10 degrees (or 0.174533 radians) is 0.984808
Tangent: 10 degrees (or 0.174533 radians) is 0.176327

Arc Sine: 0.173648 is 10 degrees (or 0.174533 radians)
Arc CoSine: 0.984808 is 10 degrees (or 0.174533 radians)
Arc Tangent: 0.176327 is 10 degrees (or 0.174533 radians)

Sine: 45 degrees (or 0.785398 radians) is 0.707107
Cosine: 45 degrees (or 0.785398 radians) is 0.707107
Tangent: 45 degrees (or 0.785398 radians) is 1

Arc Sine: 0.707107 is 45 degrees (or 0.785398 radians)
Arc CoSine: 0.707107 is 45 degrees (or 0.785398 radians)
Arc Tangent: 1 is 45 degrees (or 0.785398 radians)

Sine: 90 degrees (or 1.5708 radians) is 1
Cosine: 90 degrees (or 1.5708 radians) is 6.12323e-17
Tangent: 90 degrees (or 1.5708 radians) is 16331239353195370

Arc Sine: 1 is 90 degrees (or 1.5708 radians)
Arc CoSine: 6.12323e-17 is 90 degrees (or 1.5708 radians)
Arc Tangent: 16331239353195370 is 90 degrees (or 1.5708 radians)

Sine: 190.5 degrees (or 3.32485 radians) is -0.182236
Cosine: 190.5 degrees (or 3.32485 radians) is -0.983255
Tangent: 190.5 degrees (or 3.32485 radians) is 0.185339

Arc Sine: -0.182236 is -10.5 degrees (or -0.18326 radians)
Arc CoSine: -0.983255 is 169.5 degrees (or 2.95833 radians)
Arc Tangent: 0.185339 is 10.5 degrees (or 0.18326 radians)

BASIC[edit]

Works with: QuickBasic version 4.5

QuickBasic 4.5 does not have arcsin and arccos built in. They are defined by identities found here.

pi = 3.141592653589793#
radians = pi / 4 'a.k.a. 45 degrees
degrees = 45 * pi / 180 'convert 45 degrees to radians once
PRINT SIN(radians) + " " + SIN(degrees) 'sine
PRINT COS(radians) + " " + COS(degrees) 'cosine
PRINT TAN(radians) + " " + TAN (degrees) 'tangent
'arcsin
thesin = SIN(radians)
arcsin = ATN(thesin / SQR(1 - thesin ^ 2))
PRINT arcsin + " " + arcsin * 180 / pi
'arccos
thecos = COS(radians)
arccos = 2 * ATN(SQR(1 - thecos ^ 2) / (1 + thecos))
PRINT arccos + " " + arccos * 180 / pi
PRINT ATN(TAN(radians)) + " " + ATN(TAN(radians)) * 180 / pi 'arctan

BBC BASIC[edit]

      @% = &90F : REM set column width
 
angle_radians = PI/5
angle_degrees = 36
 
PRINT SIN(angle_radians), SIN(RAD(angle_degrees))
PRINT COS(angle_radians), COS(RAD(angle_degrees))
PRINT TAN(angle_radians), TAN(RAD(angle_degrees))
 
number = 0.6
 
PRINT ASN(number), DEG(ASN(number))
PRINT ACS(number), DEG(ACS(number))
PRINT ATN(number), DEG(ATN(number))

bc[edit]

Library: bc -l
Translation of: AWK
/* t(x) = tangent of x */
define t(x) {
return s(x) / c(x)
}
 
/* y(y) = arcsine of y, domain [-1, 1], range [-pi/2, pi/2] */
define y(y) {
/* Handle angles with no tangent. */
if (y == -1) return -2 * a(1) /* -pi/2 */
if (y == 1) return 2 * a(1) /* pi/2 */
 
/* Tangent of angle is y / x, where x^2 + y^2 = 1. */
return a(y / sqrt(1 - y * y))
}
 
/* x(x) = arccosine of x, domain [-1, 1], range [0, pi] */
define x(x) {
auto a
 
/* Handle angle with no tangent. */
if (x == 0) return 2 * a(1) /* pi/2 */
 
/* Tangent of angle is y / x, where x^2 + y^2 = 1. */
a = a(sqrt(1 - x * x) / x)
if (a < 0) {
return a + 4 * a(1) /* add pi */
} else {
return a
}
}
 
 
scale = 50
p = 4 * a(1) /* pi */
d = p / 180 /* one degree in radians */
 
"Using radians:
"
" sin(-pi / 6) = "; s(-p / 6)
" cos(3 * pi / 4) = "; c(3 * p / 4)
" tan(pi / 3) = "; t(p / 3)
" asin(-1 / 2) = "; y(-1 / 2)
" acos(-sqrt(2) / 2) = "; x(-sqrt(2) / 2)
" atan(sqrt(3)) = "; a(sqrt(3))
 
"Using degrees:
"
" sin(-30) = "; s(-30 * d)
" cos(135) = "; c(135 * d)
" tan(60) = "; t(60 * d)
" asin(-1 / 2) = "; y(-1 / 2) / d
" acos(-sqrt(2) / 2) = "; x(-sqrt(2) / 2) / d
" atan(sqrt(3)) = "; a(sqrt(3)) / d
 
quit
Output:
Using radians:
  sin(-pi / 6) = -.49999999999999999999999999999999999999999999999999
  cos(3 * pi / 4) = -.70710678118654752440084436210484903928483593768845
  tan(pi / 3) = 1.73205080756887729352744634150587236694280525381032
  asin(-1 / 2) = -.52359877559829887307710723054658381403286156656251
  acos(-sqrt(2) / 2) = 2.35619449019234492884698253745962716314787704953131
  atan(sqrt(3)) = 1.04719755119659774615421446109316762806572313312503
Using degrees:
  sin(-30) = -.49999999999999999999999999999999999999999999999981
  cos(135) = -.70710678118654752440084436210484903928483593768778
  tan(60) = 1.73205080756887729352744634150587236694280525380865
  asin(-1 / 2) = -30.00000000000000000000000000000000000000000000001203
  acos(-sqrt(2) / 2) = 135.00000000000000000000000000000000000000000000005500
  atan(sqrt(3)) = 60.00000000000000000000000000000000000000000000002463

C[edit]

#include <math.h>
#include <stdio.h>
 
int main() {
double pi = 4 * atan(1);
/*Pi / 4 is 45 degrees. All answers should be the same.*/
double radians = pi / 4;
double degrees = 45.0;
double temp;
/*sine*/
printf("%f %f\n", sin(radians), sin(degrees * pi / 180));
/*cosine*/
printf("%f %f\n", cos(radians), cos(degrees * pi / 180));
/*tangent*/
printf("%f %f\n", tan(radians), tan(degrees * pi / 180));
/*arcsine*/
temp = asin(sin(radians));
printf("%f %f\n", temp, temp * 180 / pi);
/*arccosine*/
temp = acos(cos(radians));
printf("%f %f\n", temp, temp * 180 / pi);
/*arctangent*/
temp = atan(tan(radians));
printf("%f %f\n", temp, temp * 180 / pi);
 
return 0;
}
Output:
0.707107 0.707107
0.707107 0.707107
1.000000 1.000000
0.785398 45.000000
0.785398 45.000000
0.785398 45.000000

C++[edit]

#include <iostream>
#include <cmath>
 
#ifdef M_PI // defined by all POSIX systems and some non-POSIX ones
double const pi = M_PI;
#else
double const pi = 4*std::atan(1);
#endif
 
double const degree = pi/180;
 
int main()
{
std::cout << "=== radians ===\n";
std::cout << "sin(pi/3) = " << std::sin(pi/3) << "\n";
std::cout << "cos(pi/3) = " << std::cos(pi/3) << "\n";
std::cout << "tan(pi/3) = " << std::tan(pi/3) << "\n";
std::cout << "arcsin(1/2) = " << std::asin(0.5) << "\n";
std::cout << "arccos(1/2) = " << std::acos(0.5) << "\n";
std::cout << "arctan(1/2) = " << std::atan(0.5) << "\n";
 
std::cout << "\n=== degrees ===\n";
std::cout << "sin(60°) = " << std::sin(60*degree) << "\n";
std::cout << "cos(60°) = " << std::cos(60*degree) << "\n";
std::cout << "tan(60°) = " << std::tan(60*degree) << "\n";
std::cout << "arcsin(1/2) = " << std::asin(0.5)/degree << \n";
std::cout << "arccos(1/2) = " << std::acos(0.5)/degree << \n";
std::cout << "arctan(1/2) = " << std::atan(0.5)/degree << \n";
 
return 0;
}

C#[edit]

using System;
 
namespace RosettaCode {
class Program {
static void Main(string[] args) {
Console.WriteLine("=== radians ===");
Console.WriteLine("sin (pi/3) = {0}", Math.Sin(Math.PI / 3));
Console.WriteLine("cos (pi/3) = {0}", Math.Cos(Math.PI / 3));
Console.WriteLine("tan (pi/3) = {0}", Math.Tan(Math.PI / 3));
Console.WriteLine("arcsin (1/2) = {0}", Math.Asin(0.5));
Console.WriteLine("arccos (1/2) = {0}", Math.Acos(0.5));
Console.WriteLine("arctan (1/2) = {0}", Math.Atan(0.5));
Console.WriteLine("");
Console.WriteLine("=== degrees ===");
Console.WriteLine("sin (60) = {0}", Math.Sin(60 * Math.PI / 180));
Console.WriteLine("cos (60) = {0}", Math.Cos(60 * Math.PI / 180));
Console.WriteLine("tan (60) = {0}", Math.Tan(60 * Math.PI / 180));
Console.WriteLine("arcsin (1/2) = {0}", Math.Asin(0.5) * 180/ Math.PI);
Console.WriteLine("arccos (1/2) = {0}", Math.Acos(0.5) * 180 / Math.PI);
Console.WriteLine("arctan (1/2) = {0}", Math.Atan(0.5) * 180 / Math.PI);
 
Console.ReadLine();
}
}
}

Clojure[edit]

Translation of: fortran
(ns user
(:require [clojure.contrib.generic.math-functions :as generic]))
 
;(def pi Math/PI)
(def pi (* 4 (atan 1)))
(def dtor (/ pi 180))
(def rtod (/ 180 pi))
(def radians (/ pi 4))
(def degrees 45)
 
(println (str (sin radians) " " (sin (* degrees dtor))))
(println (str (cos radians) " " (cos (* degrees dtor))))
(println (str (tan radians) " " (tan (* degrees dtor))))
(println (str (asin (sin radians) ) " " (* (asin (sin (* degrees dtor))) rtod)))
(println (str (acos (cos radians) ) " " (* (acos (cos (* degrees dtor))) rtod)))
(println (str (atan (tan radians) ) " " (* (atan (tan (* degrees dtor))) rtod)))
Output:
(matches that of Java)
0.7071067811865475 0.7071067811865475
0.7071067811865476 0.7071067811865476
0.9999999999999999 0.9999999999999999
0.7853981633974482 44.99999999999999
0.7853981633974483 45.0
0.7853981633974483 45.0

COBOL[edit]

       IDENTIFICATION DIVISION.
PROGRAM-ID. Trig.
 
DATA DIVISION.
WORKING-STORAGE SECTION.
01 Pi-Third USAGE COMP-2.
01 Degree USAGE COMP-2.
 
01 60-Degrees USAGE COMP-2.
 
01 Result USAGE COMP-2.
 
PROCEDURE DIVISION.
COMPUTE Pi-Third = FUNCTION PI / 3
 
DISPLAY "Radians:"
DISPLAY " Sin(π / 3) = " FUNCTION SIN(Pi-Third)
DISPLAY " Cos(π / 3) = " FUNCTION COS(Pi-Third)
DISPLAY " Tan(π / 3) = " FUNCTION TAN(Pi-Third)
DISPLAY " Asin(0.5) = " FUNCTION ASIN(0.5)
DISPLAY " Acos(0.5) = " FUNCTION ACOS(0.5)
DISPLAY " Atan(0.5) = " FUNCTION ATAN(0.5)
 
COMPUTE Degree = FUNCTION PI / 180
COMPUTE 60-Degrees = Degree * 60
 
DISPLAY "Degrees:"
DISPLAY " Sin(60°) = " FUNCTION SIN(60-Degrees)
DISPLAY " Cos(60°) = " FUNCTION COS(60-Degrees)
DISPLAY " Tan(60°) = " FUNCTION TAN(60-Degrees)
COMPUTE Result = FUNCTION ASIN(0.5) / 60
DISPLAY " Asin(0.5) = " Result
COMPUTE Result = FUNCTION ACOS(0.5) / 60
DISPLAY " Acos(0.5) = " Result
COMPUTE Result = FUNCTION ATAN(0.5) / 60
DISPLAY " Atan(0.5) = " Result
 
GOBACK
.
Output:
Radians:
  Sin(π / 3)  = +0.86602540368613976
  Cos(π / 3)  = +0.50000000017025856
  Tan(π / 3)  = 1.732050806782486241
  Asin(0.5) = +0.52359877559829897
  Acos(0.5) = 1.04719755119659785
  Atan(0.5) = +0.52359877559829897
Degrees:
  Sin(60°)  = +0.86602538768613932
  Cos(60°)  = +0.50000002788307131
  Tan(60°)  = 1.732050678782493636
  Asin(0.5) = 0.008726645999999999
  Acos(0.5) = 0.017453291999999999
  Atan(0.5) = 0.007727460000000000

Common Lisp[edit]

(defun deg->rad (x) (* x (/ pi 180)))
(defun rad->deg (x) (* x (/ 180 pi)))
 
(mapc (lambda (x) (format t "~s => ~s~%" x (eval x)))
'((sin (/ pi 4))
(sin (deg->rad 45))
(cos (/ pi 6))
(cos (deg->rad 30))
(tan (/ pi 3))
(tan (deg->rad 60))
(asin 1)
(rad->deg (asin 1))
(acos 1/2)
(rad->deg (acos 1/2))
(atan 15)
(rad->deg (atan 15))))

D[edit]

Translation of: C
void main() {
import std.stdio, std.math;
 
enum degrees = 45.0L;
enum t0 = degrees * PI / 180.0L;
writeln("Reference: 0.7071067811865475244008");
writefln("Sine:  %.20f  %.20f", PI_4.sin, t0.sin);
writefln("Cosine:  %.20f  %.20f", PI_4.cos, t0.cos);
writefln("Tangent:  %.20f  %.20f", PI_4.tan, t0.tan);
 
writeln;
writeln("Reference: 0.7853981633974483096156");
immutable real t1 = PI_4.sin.asin;
writefln("Arcsine:  %.20f %.20f", t1, t1 * 180.0L / PI);
 
immutable real t2 = PI_4.cos.acos;
writefln("Arccosine:  %.20f %.20f", t2, t2 * 180.0L / PI);
 
immutable real t3 = PI_4.tan.atan;
writefln("Arctangent: %.20f %.20f", t3, t3 * 180.0L / PI);
}
Output:
Reference:  0.7071067811865475244008
Sine:       0.70710678118654752442  0.70710678118654752442
Cosine:     0.70710678118654752438  0.70710678118654752438
Tangent:    1.00000000000000000000  1.00000000000000000000

Reference:  0.7853981633974483096156
Arcsine:    0.78539816339744830970 45.00000000000000000400
Arccosine:  0.78539816339744830961 45.00000000000000000000
Arctangent: 0.78539816339744830961 45.00000000000000000000

E[edit]

Translation of: ALGOL 68
def pi := (-1.0).acos()
 
def radians := pi / 4.0
def degrees := 45.0
 
def d2r := (pi/180).multiply
def r2d := (180/pi).multiply
 
println(`$\
${radians.sin()} ${d2r(degrees).sin()}
${radians.cos()} ${d2r(degrees).cos()}
${radians.tan()} ${d2r(degrees).tan()}
${def asin := radians.sin().asin()} ${r2d(asin)}
${def acos := radians.cos().acos()} ${r2d(acos)}
${def atan := radians.tan().atan()} ${r2d(atan)}
`
)
Output:
0.7071067811865475 0.7071067811865475
0.7071067811865476 0.7071067811865476
0.9999999999999999 0.9999999999999999
0.7853981633974482 44.99999999999999
0.7853981633974483 45.0
0.7853981633974483 45.0

Elena[edit]

Translation of: C++
import system'math.
import extensions.
 
program =
[
console printLine("Radians:").
console printLine("sin(π/3) = ",(pi_value/3) sin).
console printLine("cos(π/3) = ",(pi_value/3) cos).
console printLine("tan(π/3) = ",(pi_value/3) tan).
console printLine("arcsin(1/2) = ",0.5r arcsin).
console printLine("arccos(1/2) = ",0.5r arccos).
console printLine("arctan(1/2) = ",0.5r arctan).
console printLine.
 
console printLine("Degrees:").
console printLine("sin(60º) = ",60.0r radian; sin).
console printLine("cos(60º) = ",60.0r radian; cos).
console printLine("tan(60º) = ",60.0r radian; tan).
console printLine("arcsin(1/2) = ",0.5r arcsin; degree,"º").
console printLine("arccos(1/2) = ",0.5r arccos; degree,"º").
console printLine("arctan(1/2) = ",0.5r arctan; degree,"º").
 
console readChar.
].

Elixir[edit]

Translation of: Erlang
iex(61)> deg = 45
45
iex(62)> rad = :math.pi / 4
0.7853981633974483
iex(63)> :math.sin(deg * :math.pi / 180) == :math.sin(rad)
true
iex(64)> :math.cos(deg * :math.pi / 180) == :math.cos(rad)
true
iex(65)> :math.tan(deg * :math.pi / 180) == :math.tan(rad)
true
iex(66)> temp = :math.acos(:math.cos(rad))
0.7853981633974483
iex(67)> temp * 180 / :math.pi == deg
true
iex(68)> temp = :math.atan(:math.tan(rad))
0.7853981633974483
iex(69)> temp * 180 / :math.pi == deg
true

Erlang[edit]

Translation of: C
 
Deg=45.
Rad=math:pi()/4.
 
math:sin(Deg * math:pi() / 180)==math:sin(Rad).
 
Output:
true
 
math:cos(Deg * math:pi() / 180)==math:cos(Rad).
 
Output:
true
 
math:tan(Deg * math:pi() / 180)==math:tan(Rad).
 
Output:
true
 
Temp = math:acos(math:cos(Rad)).
Temp * 180 / math:pi()==Deg.
 
Output:
true
 
Temp = math:atan(math:tan(Rad)).
Temp * 180 / math:pi()==Deg.
 
Output:
true

Fantom[edit]

Fantom's Float library includes all six trigonometric functions, which assume the number is in radians.
Methods are provided to convert: toDegrees and toRadians.

 
class Main
{
public static Void main ()
{
Float r := Float.pi / 4
echo (r.sin)
echo (r.cos)
echo (r.tan)
echo (r.asin)
echo (r.acos)
echo (r.atan)
// and from degrees
echo (45.0f.toRadians.sin)
echo (45.0f.toRadians.cos)
echo (45.0f.toRadians.tan)
echo (45.0f.toRadians.asin)
echo (45.0f.toRadians.acos)
echo (45.0f.toRadians.atan)
}
}
 

Forth[edit]

45e  pi f* 180e f/     \ radians
 
cr fdup fsin f. \ also available: fsincos ( r -- sin cos )
cr fdup fcos f.
cr fdup ftan f.
cr fdup fasin f.
cr fdup facos f.
cr fatan f. \ also available: fatan2 ( r1 r2 -- atan[r1/r2] )

Fortran[edit]

Trigonometic functions expect arguments in radians so degrees require conversion

PROGRAM Trig
 
REAL pi, dtor, rtod, radians, degrees
 
pi = 4.0 * ATAN(1.0)
dtor = pi / 180.0
rtod = 180.0 / pi
radians = pi / 4.0
degrees = 45.0
 
WRITE(*,*) SIN(radians), SIN(degrees*dtor)
WRITE(*,*) COS(radians), COS(degrees*dtor)
WRITE(*,*) TAN(radians), TAN(degrees*dtor)
WRITE(*,*) ASIN(SIN(radians)), ASIN(SIN(degrees*dtor))*rtod
WRITE(*,*) ACOS(COS(radians)), ACOS(COS(degrees*dtor))*rtod
WRITE(*,*) ATAN(TAN(radians)), ATAN(TAN(degrees*dtor))*rtod
 
END PROGRAM Trig
Output:
 0.707107   0.707107
 0.707107   0.707107
  1.00000    1.00000
 0.785398    45.0000
 0.785398    45.0000
 0.785398    45.0000

The following trigonometric functions are also available

 ATAN2(y,x) ! Arctangent(y/x), ''-pi < result <= +pi'' 
SINH(x) ! Hyperbolic sine
COSH(x) ! Hyperbolic cosine
TANH(x) ! Hyperbolic tangent

But, for those with access to fatter Fortran function libraries, trigonometrical functions working in degrees are also available.

 
Calculate various trigonometric functions from the Fortran library.
INTEGER BIT(32),B,IP !Stuff for bit fiddling.
INTEGER ENUFF,I !Step through the test angles.
PARAMETER (ENUFF = 17) !A selection of special values.
INTEGER ANGLE(ENUFF) !All in whole degrees.
DATA ANGLE/0,30,45,60,90,120,135,150,180, !Here they are.
1 210,225,240,270,300,315,330,360/ !Thus check angle folding.
REAL PI,DEG2RAD !Special numbers.
REAL D,R,FD,FR,AD,AR !Degree, Radian, F(D), F(R), inverses.
PI = 4*ATAN(1.0) !SINGLE PRECISION 1·0.
DEG2RAD = PI/180 !Limited precision here too for a transcendental number.
Case the first: sines.
WRITE (6,10) ("Sin", I = 1,4) !Supply some names.
10 FORMAT (" Deg.",A7,"(Deg)",A7,"(Rad) Rad - Deg", !Ah, layout.
1 6X,"Arc",A3,"D",6X,"Arc",A3,"R",9X,"Diff")
DO I = 1,ENUFF !Step through the test values.
D = ANGLE(I) !The angle in degrees, in floating point.
R = D*DEG2RAD !Approximation, in radians.
FD = SIND(D); AD = ASIND(FD) !Functions working in degrees.
FR = SIN(R); AR = ASIN(FR)/DEG2RAD !Functions working in radians.
WRITE (6,11) INT(D),FD,FR,FR - FD,AD,AR,AR - AD !Results.
11 FORMAT (I4,":",3F12.8,3F13.7) !Ah, alignment with FORMAT 10...
END DO !On to the next test value.
Case the second: cosines.
WRITE (6,10) ("Cos", I = 1,4)
DO I = 1,ENUFF
D = ANGLE(I)
R = D*DEG2RAD
FD = COSD(D); AD = ACOSD(FD)
FR = COS(R); AR = ACOS(FR)/DEG2RAD
WRITE (6,11) INT(D),FD,FR,FR - FD,AD,AR,AR - AD
END DO
Case the third: tangents.
WRITE (6,10) ("Tan", I = 1,4)
DO I = 1,ENUFF
D = ANGLE(I)
R = D*DEG2RAD
FD = TAND(D); AD = ATAND(FD)
FR = TAN(R); AR = ATAN(FR)/DEG2RAD
WRITE (6,11) INT(D),FD,FR,FR - FD,AD,AR,AR - AD
END DO
WRITE (6,*) "...Special deal for 90 degrees..."
D = 90
R = D*DEG2RAD
FD = TAND(D); AD = ATAND(FD)
FR = TAN(R); AR = ATAN(FR)/DEG2RAD
WRITE (6,*) "TanD =",FD,"Atan =",AD
WRITE (6,*) "TanR =",FR,"Atan =",AR
Convert PI to binary...
PI = PI - 3 !I know it starts with three, and I need the fractional part.
BIT(1:2) = 1 !So, the binary is 11. something.
B = 2 !Two bits known.
DO I = 1,26 !For single precision, more than enough additional bits.
PI = PI*2 !Hoist a bit to the hot spot.
IP = PI !The integral part.
PI = PI - IP !Remove it from the work in progress.
B = B + 1 !Another bit bitten.
BIT(B) = IP !Place it.
END DO !On to the next.
WRITE (6,20) BIT(1:B) !Reveal the bits.
20 FORMAT (" Pi ~ ",2I1,".",66I1) !A known format.
WRITE (6,*) " = 11.00100100001111110110101010001000100001..." !But actually...
END !So much for that.
 

Output:

Deg.    Sin(Deg)    Sin(Rad)   Rad - Deg      ArcSinD      ArcSinR         Diff
  0:  0.00000000  0.00000000  0.00000000    0.0000000    0.0000000    0.0000000
 30:  0.50000000  0.50000000  0.00000000   30.0000000   30.0000000    0.0000000
 45:  0.70710677  0.70710677  0.00000000   45.0000000   45.0000000    0.0000000
 60:  0.86602539  0.86602545  0.00000006   60.0000000   60.0000038    0.0000038
 90:  1.00000000  1.00000000  0.00000000   90.0000000   90.0000000    0.0000000
120:  0.86602539  0.86602539  0.00000000   60.0000000   60.0000000    0.0000000
135:  0.70710677  0.70710677  0.00000000   45.0000000   45.0000000    0.0000000
150:  0.50000000  0.50000006  0.00000006   30.0000000   30.0000038    0.0000038
180:  0.00000000 -0.00000009 -0.00000009    0.0000000   -0.0000050   -0.0000050
210: -0.50000000 -0.49999997  0.00000003  -30.0000000  -29.9999981    0.0000019
225: -0.70710677 -0.70710671  0.00000006  -45.0000000  -44.9999962    0.0000038
240: -0.86602539 -0.86602545 -0.00000006  -60.0000000  -60.0000038   -0.0000038
270: -1.00000000 -1.00000000  0.00000000  -90.0000000  -90.0000000    0.0000000
300: -0.86602539 -0.86602545 -0.00000006  -60.0000000  -60.0000038   -0.0000038
315: -0.70710677 -0.70710689 -0.00000012  -45.0000000  -45.0000076   -0.0000076
330: -0.50000000 -0.50000018 -0.00000018  -30.0000000  -30.0000114   -0.0000114
360:  0.00000000  0.00000017  0.00000017    0.0000000    0.0000100    0.0000100
Deg.    Cos(Deg)    Cos(Rad)   Rad - Deg      ArcCosD      ArcCosR         Diff
  0:  1.00000000  1.00000000  0.00000000    0.0000000    0.0000000    0.0000000
 30:  0.86602539  0.86602539  0.00000000   30.0000019   30.0000019    0.0000000
 45:  0.70710677  0.70710677  0.00000000   45.0000000   45.0000000    0.0000000
 60:  0.50000000  0.49999997 -0.00000003   60.0000000   60.0000038    0.0000038
 90:  0.00000000 -0.00000004 -0.00000004   90.0000000   90.0000000    0.0000000
120: -0.50000000 -0.50000006 -0.00000006  120.0000000  120.0000076    0.0000076
135: -0.70710677 -0.70710677  0.00000000  135.0000000  135.0000000    0.0000000
150: -0.86602539 -0.86602539  0.00000000  150.0000000  150.0000000    0.0000000
180: -1.00000000 -1.00000000  0.00000000  180.0000000  180.0000000    0.0000000
210: -0.86602539 -0.86602539  0.00000000  150.0000000  150.0000000    0.0000000
225: -0.70710677 -0.70710683 -0.00000006  135.0000000  135.0000000    0.0000000
240: -0.50000000 -0.49999991  0.00000009  120.0000000  119.9999924   -0.0000076
270:  0.00000000  0.00000001  0.00000001   90.0000000   90.0000000    0.0000000
300:  0.50000000  0.49999991 -0.00000009   60.0000000   60.0000076    0.0000076
315:  0.70710677  0.70710665 -0.00000012   45.0000000   45.0000114    0.0000114
330:  0.86602539  0.86602533 -0.00000006   30.0000019   30.0000095    0.0000076
360:  1.00000000  1.00000000  0.00000000    0.0000000    0.0000000    0.0000000
Deg.    Tan(Deg)    Tan(Rad)   Rad - Deg      ArcTanD      ArcTanR         Diff
  0:  0.00000000  0.00000000  0.00000000    0.0000000    0.0000000    0.0000000
 30:  0.57735026  0.57735026  0.00000000   30.0000000   30.0000000    0.0000000
 45:  1.00000000  1.00000000  0.00000000   45.0000000   45.0000000    0.0000000
 60:  1.73205078  1.73205090  0.00000012   60.0000000   60.0000000    0.0000000
 90:************************************   90.0000000  -90.0000000 -180.0000000
120: -1.73205078 -1.73205054  0.00000024  -60.0000000  -59.9999962    0.0000038
135: -1.00000000 -1.00000000  0.00000000  -45.0000000  -45.0000000    0.0000000
150: -0.57735026 -0.57735032 -0.00000006  -30.0000000  -30.0000019   -0.0000019
180:  0.00000000  0.00000009  0.00000009    0.0000000    0.0000050    0.0000050
210:  0.57735026  0.57735026  0.00000000   30.0000000   30.0000000    0.0000000
225:  1.00000000  0.99999988 -0.00000012   45.0000000   44.9999962   -0.0000038
240:  1.73205078  1.73205125  0.00000048   60.0000000   60.0000076    0.0000076
270:************************************   90.0000000  -90.0000000 -180.0000000
300: -1.73205078 -1.73205113 -0.00000036  -60.0000000  -60.0000038   -0.0000038
315: -1.00000000 -1.00000024 -0.00000024  -45.0000000  -45.0000076   -0.0000076
330: -0.57735026 -0.57735056 -0.00000030  -30.0000000  -30.0000134   -0.0000134
360:  0.00000000  0.00000017  0.00000017    0.0000000    0.0000100    0.0000100
...Special deal for 90 degrees...
TanD =  1.6331778E+16 Atan =   90.00000    
TanR = -2.2877332E+07 Atan =  -90.00000    
Pi ~ 11.00100100001111110110110000
   = 11.00100100001111110110101010001000100001...

Notice that the calculations in radians are less accurate. Firstly, pi cannot be represented exactly and secondly, the conversion factor of pi/180 or 180/pi adds further to the error. The degree-based functions obviously can fold their angles using exact arithmetic (though ACosD has surprising trouble with 30°) and so 360° is the same as 0°, unlike the case with radians. TanD(90°) should yield Infinity (but, which sign?) but perhaps this latter-day feature of computer floating-point was not included. In any case, Tan(90° in radians) faces the problem that its parameter will not in fact be pi/2 but some value just over (or under), and likewise with double precision and quadruple precision and any other finite precision.

FreeBASIC[edit]

Translation of: C
' FB 1.05.0 Win64
 
Const pi As Double = 4 * Atn(1)
Dim As Double radians = pi / 4
Dim As Double degrees = 45.0 '' equivalent in degrees
Dim As Double temp
 
Print "Radians  : "; radians, " ";
Print "Degrees  : "; degrees
Print
Print "Sine  : "; Sin(radians), Sin(degrees * pi / 180)
Print "Cosine  : "; Cos(radians), Cos(degrees * pi / 180)
Print "Tangent  : "; Tan(radians), Tan(degrees * pi / 180)
Print
temp = ASin(Sin(radians))
Print "Arc Sine  : "; temp, temp * 180 / pi
temp = ACos(Cos(radians))
Print "Arc Cosine  : "; temp, temp * 180 / pi
temp = Atn(Tan(radians))
Print "Arc Tangent : "; temp, temp * 180 / pi
Sleep
Output:
Radians     :  0.7853981633974483          Degrees     :  45

Sine        :  0.7071067811865475          0.7071067811865475
Cosine      :  0.7071067811865476          0.7071067811865476
Tangent     :  0.9999999999999999          0.9999999999999999

Arc Sine    :  0.7853981633974482          44.99999999999999
Arc Cosine  :  0.7853981633974483          45
Arc Tangent :  0.7853981633974483          45

F#[edit]

open NUnit.Framework
open FsUnit
 
// radian
 
[<Test>]
let ``Verify that sin pi returns 0`` () =
let x = System.Math.Sin System.Math.PI
System.Math.Round(x,5) |> should equal 0
 
[<Test>]
let ``Verify that cos pi returns -1`` () =
let x = System.Math.Cos System.Math.PI
System.Math.Round(x,5) |> should equal -1
 
[<Test>]
let ``Verify that tan pi returns 0`` () =
let x = System.Math.Tan System.Math.PI
System.Math.Round(x,5) |> should equal 0
 
[<Test>]
let ``Verify that sin pi/2 returns 1`` () =
let x = System.Math.Sin (System.Math.PI / 2.0)
System.Math.Round(x,5) |> should equal 1
 
[<Test>]
let ``Verify that cos pi/2 returns -1`` () =
let x = System.Math.Cos (System.Math.PI / 2.0)
System.Math.Round(x,5) |> should equal 0
 
[<Test>]
let ``Verify that sin pi/3 returns sqrt 3/2`` () =
let actual = System.Math.Sin (System.Math.PI / 3.0)
let expected = System.Math.Round((System.Math.Sqrt 3.0) / 2.0, 5)
System.Math.Round(actual,5) |> should equal expected
 
[<Test>]
let ``Verify that cos pi/3 returns -1`` () =
let x = System.Math.Cos (System.Math.PI / 3.0)
System.Math.Round(x,5) |> should equal 0.5
 
[<Test>]
let ``Verify that cos and sin of pi/4 return same value`` () =
let c = System.Math.Cos (System.Math.PI / 4.0)
let s = System.Math.Sin (System.Math.PI / 4.0)
System.Math.Round(c,5) = System.Math.Round(s,5) |> should be True
 
[<Test>]
let ``Verify that acos pi/3 returns 1/2`` () =
let actual = System.Math.Acos 0.5
let expected = System.Math.Round((System.Math.PI / 3.0),5)
System.Math.Round(actual,5) |> should equal expected
 
[<Test>]
let ``Verify that asin 1 returns pi/2`` () =
let actual = System.Math.Asin 1.0
let expected = System.Math.Round((System.Math.PI / 2.0),5)
System.Math.Round(actual,5) |> should equal expected
 
[<Test>]
let ``Verify that atan 0 returns 0`` () =
let actual = System.Math.Atan 0.0
let expected = System.Math.Round(0.0,5)
System.Math.Round(actual,5) |> should equal expected
 
// degree
 
let toRadians d = d * System.Math.PI / 180.0
 
[<Test>]
let ``Verify that pi is 180 degrees`` () =
toRadians 180.0 |> should equal System.Math.PI
 
[<Test>]
let ``Verify that pi/2 is 90 degrees`` () =
toRadians 90.0 |> should equal (System.Math.PI / 2.0)
 
[<Test>]
let ``Verify that pi/3 is 60 degrees`` () =
toRadians 60.0 |> should equal (System.Math.PI / 3.0)
 
[<Test>]
let ``Verify that sin 180 returns 0`` () =
let x = System.Math.Sin (toRadians 180.0)
System.Math.Round(x,5) |> should equal 0
 
[<Test>]
let ``Verify that cos 180 returns -1`` () =
let x = System.Math.Cos (toRadians 180.0)
System.Math.Round(x,5) |> should equal -1
 
[<Test>]
let ``Verify that tan 180 returns 0`` () =
let x = System.Math.Tan (toRadians 180.0)
System.Math.Round(x,5) |> should equal 0
 
[<Test>]
let ``Verify that sin 90 returns 1`` () =
let x = System.Math.Sin (toRadians 90.0)
System.Math.Round(x,5) |> should equal 1
 
[<Test>]
let ``Verify that cos 90 returns -1`` () =
let x = System.Math.Cos (toRadians 90.0)
System.Math.Round(x,5) |> should equal 0
 
[<Test>]
let ``Verify that sin 60 returns sqrt 3/2`` () =
let actual = System.Math.Sin (toRadians 60.0)
let expected = System.Math.Round((System.Math.Sqrt 3.0) / 2.0, 5)
System.Math.Round(actual,5) |> should equal expected
 
[<Test>]
let ``Verify that cos 60 returns -1`` () =
let x = System.Math.Cos (toRadians 60.0)
System.Math.Round(x,5) |> should equal 0.5
 
[<Test>]
let ``Verify that cos and sin of 45 return same value`` () =
let c = System.Math.Cos (toRadians 45.0)
let s = System.Math.Sin (toRadians 45.0)
System.Math.Round(c,5) = System.Math.Round(s,5) |> should be True

GAP[edit]

# GAP has an improved floating-point support since version 4.5
 
Pi := Acos(-1.0);
 
# Or use the built-in constant:
Pi := FLOAT.PI;
 
r := Pi / 5.0;
d := 36;
 
Deg := x -> x * Pi / 180;
 
Sin(r); Asin(last);
Sin(Deg(d)); Asin(last);
Cos(r); Acos(last);
Cos(Deg(d)); Acos(last);
Tan(r); Atan(last);
Tan(Deg(d)); Atan(last);

Go[edit]

The Go math package provides the constant pi and the six trigonometric functions called for by the task. The functions all use the float64 type and work in radians. It also provides a Sincos function.

package main
 
import (
"fmt"
"math"
)
 
const d = 30.
const r = d * math.Pi / 180
 
var s = .5
var c = math.Sqrt(3) / 2
var t = 1 / math.Sqrt(3)
 
func main() {
fmt.Printf("sin(%9.6f deg) = %f\n", d, math.Sin(d*math.Pi/180))
fmt.Printf("sin(%9.6f rad) = %f\n", r, math.Sin(r))
fmt.Printf("cos(%9.6f deg) = %f\n", d, math.Cos(d*math.Pi/180))
fmt.Printf("cos(%9.6f rad) = %f\n", r, math.Cos(r))
fmt.Printf("tan(%9.6f deg) = %f\n", d, math.Tan(d*math.Pi/180))
fmt.Printf("tan(%9.6f rad) = %f\n", r, math.Tan(r))
fmt.Printf("asin(%f) = %9.6f deg\n", s, math.Asin(s)*180/math.Pi)
fmt.Printf("asin(%f) = %9.6f rad\n", s, math.Asin(s))
fmt.Printf("acos(%f) = %9.6f deg\n", c, math.Acos(c)*180/math.Pi)
fmt.Printf("acos(%f) = %9.6f rad\n", c, math.Acos(c))
fmt.Printf("atan(%f) = %9.6f deg\n", t, math.Atan(t)*180/math.Pi)
fmt.Printf("atan(%f) = %9.6f rad\n", t, math.Atan(t))
}
Output:
sin(30.000000 deg) = 0.500000
sin( 0.523599 rad) = 0.500000
cos(30.000000 deg) = 0.866025
cos( 0.523599 rad) = 0.866025
tan(30.000000 deg) = 0.577350
tan( 0.523599 rad) = 0.577350
asin(0.500000) = 30.000000 deg
asin(0.500000) =  0.523599 rad
acos(0.866025) = 30.000000 deg
acos(0.866025) =  0.523599 rad
atan(0.577350) = 30.000000 deg
atan(0.577350) =  0.523599 rad

Groovy[edit]

Trig functions use radians, degrees must be converted to/from radians

def radians = Math.PI/4
def degrees = 45
 
def d2r = { it*Math.PI/180 }
def r2d = { it*180/Math.PI }
 
println "sin(\u03C0/4) = ${Math.sin(radians)} == sin(45\u00B0) = ${Math.sin(d2r(degrees))}"
println "cos(\u03C0/4) = ${Math.cos(radians)} == cos(45\u00B0) = ${Math.cos(d2r(degrees))}"
println "tan(\u03C0/4) = ${Math.tan(radians)} == tan(45\u00B0) = ${Math.tan(d2r(degrees))}"
println "asin(\u221A2/2) = ${Math.asin(2**(-0.5))} == asin(\u221A2/2)\u00B0 = ${r2d(Math.asin(2**(-0.5)))}\u00B0"
println "acos(\u221A2/2) = ${Math.acos(2**(-0.5))} == acos(\u221A2/2)\u00B0 = ${r2d(Math.acos(2**(-0.5)))}\u00B0"
println "atan(1) = ${Math.atan(1)} == atan(1)\u00B0 = ${r2d(Math.atan(1))}\u00B0"
Output:
sin(π/4) = 0.7071067811865475  == sin(45°) = 0.7071067811865475
cos(π/4) = 0.7071067811865476  == cos(45°) = 0.7071067811865476
tan(π/4) = 0.9999999999999999  == tan(45°) = 0.9999999999999999
asin(√2/2) = 0.7853981633974482 == asin(√2/2)° = 44.99999999999999°
acos(√2/2) = 0.7853981633974484 == acos(√2/2)° = 45.00000000000001°
atan(1) = 0.7853981633974483 == atan(1)° = 45.0°

Haskell[edit]

Trigonometric functions use radians; degrees require conversion.

fromDegrees :: Floating a => a -> a
fromDegrees deg = deg * pi / 180
 
toDegrees :: Floating a => a -> a
toDegrees rad = rad * 180 / pi
 
main :: IO ()
main =
mapM_
print
[ sin (pi / 6)
, sin (fromDegrees 30)
, cos (pi / 6)
, cos (fromDegrees 30)
, tan (pi / 6)
, tan (fromDegrees 30)
, asin 0.5
, toDegrees (asin 0.5)
, acos 0.5
, toDegrees (acos 0.5)
, atan 0.5
, toDegrees (atan 0.5)
]
Output:
0.49999999999999994
0.49999999999999994
0.8660254037844387
0.8660254037844387
0.5773502691896256
0.5773502691896256
0.5235987755982988
29.999999999999996
1.0471975511965976
59.99999999999999
0.46364760900080615
26.56505117707799

HicEst[edit]

Translated from Fortran:

pi = 4.0 * ATAN(1.0)
dtor = pi / 180.0
rtod = 180.0 / pi
radians = pi / 4.0
degrees = 45.0
 
WRITE(ClipBoard) SIN(radians), SIN(degrees*dtor)
WRITE(ClipBoard) COS(radians), COS(degrees*dtor)
WRITE(ClipBoard) TAN(radians), TAN(degrees*dtor)
WRITE(ClipBoard) ASIN(SIN(radians)), ASIN(SIN(degrees*dtor))*rtod
WRITE(ClipBoard) ACOS(COS(radians)), ACOS(COS(degrees*dtor))*rtod
WRITE(ClipBoard) ATAN(TAN(radians)), ATAN(TAN(degrees*dtor))*rtod
0.7071067812 0.7071067812
0.7071067812 0.7071067812
1 1
0.7853981634 45
0.7853981634 45
0.7853981634 45

SINH, COSH, TANH, and inverses are available as well.

IDL[edit]

deg = 35         ; arbitrary number of degrees
rad = !dtor*deg ; system variables !dtor and !radeg convert between rad and deg
; the trig functions receive and emit radians:
print, rad, sin(rad), asin(sin(rad))
print, cos(rad), acos(cos(rad))
print, tan(rad), atan(tan(rad)) ; etc
 
; prints the following:
; 0.610865 0.573576 0.610865
; 0.819152 0.610865
; 0.700208 0.610865
; the hyperbolic versions exist and behave as expected:
print, sinh(rad) ; etc
 
; outputs
; 0.649572
;If the input is an array, the output has the same dimensions etc as the input:
x = !dpi/[[2,3],[4,5],[6,7]] ; !dpi is a read-only sysvar = 3.1415...
print,sin(x)
 
;outputs:
; 1.0000000 0.86602540
; 0.70710678 0.58778525
; 0.50000000 0.43388374
; the trig functions behave as expected for complex arguments:
x = complex(1,2)
print,sin(x)
 
; outputs
; ( 3.16578, 1.95960)

Icon and Unicon[edit]

Icon and Unicon trig functions 'sin', 'cos', 'tan', 'asin', 'acos', and 'atan' operate on angles expressed in radians. Conversion functions 'dtor' and 'rtod' convert between the two systems. The example below uses string invocation to construct and call the functions:

Icon[edit]

invocable all
procedure main()
 
d := 30 # degrees
r := dtor(d) # convert to radians
 
every write(f := !["sin","cos","tan"],"(",r,")=",y := f(r)," ",fi := "a" || f,"(",y,")=",x := fi(y)," rad = ",rtod(x)," deg")
end
Output:
sin(0.5235987755982988)=0.4999999999999999 asin(0.4999999999999999)=0.5235987755982988 rad = 30.0 deg
cos(0.5235987755982988)=0.8660254037844387 acos(0.8660254037844387)=0.5235987755982987 rad = 29.99999999999999 deg
tan(0.5235987755982988)=0.5773502691896257 atan(0.5773502691896257)=0.5235987755982988 rad = 30.0 deg

Unicon[edit]

The Icon solution works in Unicon.

J[edit]

The circle functions in J include trigonometric functions. Native operation is in radians, so values in degrees involve conversion.

Sine, cosine, and tangent of a single angle, indicated as pi-over-four radians and as 45 degrees:

   (1&o. , 2&o. ,: 3&o.) (4 %~ o. 1) , 180 %~ o. 45
0.707107 0.707107
0.707107 0.707107
1 1

Arcsine, arccosine, and arctangent of one-half, in radians and degrees:

   ([ ,. 180p_1&*) (_1&o. , _2&o. ,: _3&o.) 0.5
0.523599 30
1.0472 60
0.463648 26.5651

The trig script adds cover functions for the trigonometric operations as well as verbs for converting degrees from radians (dfr) and radians from degrees (rfd)

   require 'trig'
(sin , cos ,: tan) (1p1 % 4), rfd 45
0.707107 0.707107
0.707107 0.707107
1 1
 
([ ,. dfr) (arcsin , arccos ,: arctan) 0.5
0.523599 30
1.0472 60
0.463648 26.5651

Java[edit]

Java's Math class contains all six functions and is automatically included as part of the language. The functions all accept radians only, so conversion is necessary when dealing with degrees. The Math class also has a PI constant for easy conversion.

public class Trig {
public static void main(String[] args) {
//Pi / 4 is 45 degrees. All answers should be the same.
double radians = Math.PI / 4;
double degrees = 45.0;
//sine
System.out.println(Math.sin(radians) + " " + Math.sin(Math.toRadians(degrees)));
//cosine
System.out.println(Math.cos(radians) + " " + Math.cos(Math.toRadians(degrees)));
//tangent
System.out.println(Math.tan(radians) + " " + Math.tan(Math.toRadians(degrees)));
//arcsine
double arcsin = Math.asin(Math.sin(radians));
System.out.println(arcsin + " " + Math.toDegrees(arcsin));
//arccosine
double arccos = Math.acos(Math.cos(radians));
System.out.println(arccos + " " + Math.toDegrees(arccos));
//arctangent
double arctan = Math.atan(Math.tan(radians));
System.out.println(arctan + " " + Math.toDegrees(arctan));
}
}
Output:
0.7071067811865475 0.7071067811865475
0.7071067811865476 0.7071067811865476
0.9999999999999999 0.9999999999999999
0.7853981633974482 44.99999999999999
0.7853981633974483 45.0
0.7853981633974483 45.0

JavaScript[edit]

JavaScript's Math class contains all six functions and is automatically included as part of the language. The functions all accept radians only, so conversion is necessary when dealing with degrees. The Math class also has a PI constant for easy conversion.

var
radians = Math.PI / 4, // Pi / 4 is 45 degrees. All answers should be the same.
degrees = 45.0,
sine = Math.sin(radians),
cosine = Math.cos(radians),
tangent = Math.tan(radians),
arcsin = Math.asin(sine),
arccos = Math.acos(cosine),
arctan = Math.atan(tangent);
 
// sine
window.alert(sine + " " + Math.sin(degrees * Math.PI / 180));
// cosine
window.alert(cosine + " " + Math.cos(degrees * Math.PI / 180));
// tangent
window.alert(tangent + " " + Math.tan(degrees * Math.PI / 180));
// arcsine
window.alert(arcsin + " " + (arcsin * 180 / Math.PI));
// arccosine
window.alert(arccos + " " + (arccos * 180 / Math.PI));
// arctangent
window.alert(arctan + " " + (arctan * 180 / Math.PI));

jq[edit]

jq includes the standard C-library trigonometric functions (sin, cos, tan, asin, acos, atan), but they are provided as filters as illustrated in the definition of radians below.

The trigonometric filters only accept radians, so conversion is necessary when dealing with degrees. The constant π can be defined as also shown in the following definition of radians:
 
# degrees to radians
def radians:
(-1|acos) as $pi | (. * $pi / 180);
 
def task:
(-1|acos) as $pi
| ($pi / 180) as $degrees
| "Using radians:",
" sin(-pi / 6) = \( (-$pi / 6) | sin )",
" cos(3 * pi / 4) = \( (3 * $pi / 4) | cos)",
" tan(pi / 3) = \( ($pi / 3) | tan)",
" asin(-1 / 2) = \((-1 / 2) | asin)",
" acos(-sqrt(2)/2) = \((-(2|sqrt)/2) | acos )",
" atan(sqrt(3)) = \( 3 | sqrt | atan )",
 
"Using degrees:",
" sin(-30) = \((-30 * $degrees) | sin)",
" cos(135) = \((135 * $degrees) | cos)",
" tan(60) = \(( 60 * $degrees) | tan)",
" asin(-1 / 2) = \( (-1 / 2) | asin / $degrees)",
" acos(-sqrt(2)/2) = \( (-(2|sqrt) / 2) | acos / $degrees)",
" atan(sqrt(3)) = \( (3 | sqrt) | atan / $degrees)"
;
 
task
 
Output:
Using radians:
sin(-pi / 6) = -0.49999999999999994
cos(3 * pi / 4) = -0.7071067811865475
tan(pi / 3) = 1.7320508075688767
asin(-1 / 2) = -0.5235987755982988
acos(-sqrt(2)/2) = 2.356194490192345
atan(sqrt(3)) = 1.0471975511965979
Using degrees:
sin(-30) = -0.49999999999999994
cos(135) = -0.7071067811865475
tan(60) = 1.7320508075688767
asin(-1 / 2) = -29.999999999999996
acos(-sqrt(2)/2) = 135
atan(sqrt(3)) = 60.00000000000001

Julia[edit]

# v0.6.0
 
rad = π / 4
deg = 45.0
 
@show rad deg
@show sin(rad) sin(deg2rad(deg))
@show cos(rad) cos(deg2rad(deg))
@show tan(rad) tan(deg2rad(deg))
@show asin(sin(rad)) asin(sin(rad)) |> rad2deg
@show acos(cos(rad)) acos(cos(rad)) |> rad2deg
@show atan(tan(rad)) atan(tan(rad)) |> rad2deg
Output:
rad = 0.7853981633974483
deg = 45.0
sin(rad) = 0.7071067811865475
sin(deg2rad(deg)) = 0.7071067811865475
cos(rad) = 0.7071067811865476
cos(deg2rad(deg)) = 0.7071067811865476
tan(rad) = 0.9999999999999999
tan(deg2rad(deg)) = 0.9999999999999999
asin(sin(rad)) = 0.7853981633974482
asin(sin(rad)) |> rad2deg = 44.99999999999999
acos(cos(rad)) = 0.7853981633974483
acos(cos(rad)) |> rad2deg = 45.0
atan(tan(rad)) = 0.7853981633974483
atan(tan(rad)) |> rad2deg = 45.0

Kotlin[edit]

// version 1.1.2
 
import java.lang.Math.*
 
fun main(args: Array<String>) {
val radians = Math.PI / 4.0
val degrees = 45.0
val conv = Math.PI / 180.0
val f = "%1.15f"
var inverse: Double
 
println(" Radians Degrees")
println("Angle  : ${f.format(radians)}\t ${f.format(degrees)}\n")
println("Sin  : ${f.format(sin(radians))}\t ${f.format(sin(degrees * conv))}")
println("Cos  : ${f.format(cos(radians))}\t ${f.format(cos(degrees * conv))}")
println("Tan  : ${f.format(tan(radians))}\t ${f.format(tan(degrees * conv))}\n")
inverse = asin(sin(radians))
println("ASin(Sin)  : ${f.format(inverse)}\t ${f.format(inverse / conv)}")
inverse = acos(cos(radians))
println("ACos(Cos)  : ${f.format(inverse)}\t ${f.format(inverse / conv)}")
inverse = atan(tan(radians))
println("ATan(Tan)  : ${f.format(inverse)}\t ${f.format(inverse / conv)}")
}
Output:
                Radians              Degrees
Angle      : 0.785398163397448	 45.000000000000000

Sin        : 0.707106781186548	  0.707106781186548
Cos        : 0.707106781186548	  0.707106781186548
Tan        : 1.000000000000000	  1.000000000000000

ASin(Sin)  : 0.785398163397448	 44.999999999999990
ACos(Cos)  : 0.785398163397448	 45.000000000000000
ATan(Tan)  : 0.785398163397448	 45.000000000000000

Liberty BASIC[edit]

pi = ACS(-1)
radians = pi / 4.0
rtod = 180 / pi
degrees = radians * rtod
dtor = pi / 180
 
'LB works in radians, so degrees require conversion
print "Sin: ";SIN(radians);" "; SIN(degrees*dtor)
print "Cos: ";COS(radians);" "; COS(degrees*dtor)
print "Tan: ";TAN(radians);" ";TAN(degrees*dtor)
print "- Inverse functions:"
print "Asn: ";ASN(SIN(radians));" Rad, "; ASN(SIN(degrees*dtor))*rtod;" Deg"
print "Acs: ";ACS(COS(radians));" Rad, "; ACS(COS(degrees*dtor))*rtod;" Deg"
print "Atn: ";ATN(TAN(radians));" Rad, "; ATN(TAN(degrees*dtor))*rtod;" Deg"
Output:
Sin:  0.70710678    0.70710678
Cos:  0.70710678    0.70710678
Tan:  1.0           1.0
-  Inverse functions:
Asn:   0.78539816 Rad,  45.0 Deg
Acs:   0.78539816 Rad,  45.0 Deg
Atn:   0.78539816 Rad,  45.0 Deg

[edit]

UCB Logo has sine, cosine, and arctangent; each having variants for degrees or radians.

print sin 45
print cos 45
print arctan 1
make "pi (radarctan 0 1) * 2 ; based on quadrant if uses two parameters
print radsin :pi / 4
print radcos :pi / 4
print 4 * radarctan 1


Lhogho has pi defined in its trigonometric functions. Otherwise the same as UCB Logo.

print sin 45
print cos 45
print arctan 1
print radsin pi / 4
print radcos pi / 4
print 4 * radarctan 1

Logtalk[edit]

 
:- object(trignomeric_functions).
 
:- public(show/0).
show :-
% standard trignomeric functions work with radians
write('sin(pi/4.0) = '), SIN is sin(pi/4.0), write(SIN), nl,
write('cos(pi/4.0) = '), COS is cos(pi/4.0), write(COS), nl,
write('tan(pi/4.0) = '), TAN is tan(pi/4.0), write(TAN), nl,
write('asin(sin(pi/4.0)) = '), ASIN is asin(sin(pi/4.0)), write(ASIN), nl,
write('acos(cos(pi/4.0)) = '), ACOS is acos(cos(pi/4.0)), write(ACOS), nl,
write('atan(tan(pi/4.0)) = '), ATAN is atan(tan(pi/4.0)), write(ATAN), nl,
write('atan2(3,4) = '), ATAN2 is atan2(3,4), write(ATAN2), nl.
 
:- end_object.
 
Output:
 
?- trignomeric_functions::show.
sin(pi/4.0) = 0.7071067811865475
cos(pi/4.0) = 0.7071067811865476
tan(pi/4.0) = 0.9999999999999999
asin(sin(pi/4.0)) = 0.7853981633974482
acos(cos(pi/4.0)) = 0.7853981633974483
atan(tan(pi/4.0)) = 0.7853981633974483
atan2(3,4) = 0.6435011087932844
yes
 

Lua[edit]

print(math.cos(1), math.sin(1), math.tan(1), math.atan(1), math.atan2(3, 4))

Maple[edit]

In radians:

sin(Pi/3);
cos(Pi/3);
tan(Pi/3);
Output:
> sin(Pi/3);
                                 1/2
                                3
                                ----
                                 2
> cos(Pi/3);
                                1/2

> tan(Pi/3);
                                 1/2
                                3

The equivalent in degrees with identical output:

with(Units[Standard]):
sin(60*Unit(degree));
cos(60*Unit(degree));
tan(60*Unit(degree));

Note, Maple also has secant, cosecant, and cotangent:

csc(Pi/3);
sec(Pi/3);
cot(Pi/3);

Finally, the inverse trigonometric functions:

arcsin(1);
arccos(1);
arctan(1);
Output:
> arcsin(1);
                 Pi
                ----
                 2

> arccos(1);
                  0

> arctan(1);
                 Pi
                ----
                 4

Lastly, Maple also supports the two-argument arctan plus all the hyperbolic trigonometric functions.

Mathematica[edit]

Sin[1]
Cos[1]
Tan[1]
ArcSin[1]
ArcCos[1]
ArcTan[1]
Sin[90 Degree]
Cos[90 Degree]
Tan[90 Degree]
 

MATLAB[edit]

A full list of built-in trig functions can be found in the MATLAB Documentation.

function trigExample(angleDegrees)
 
angleRadians = angleDegrees * (pi/180);
 
disp(sprintf('sin(%f)= %f\nasin(%f)= %f',[angleRadians sin(angleRadians) sin(angleRadians) asin(sin(angleRadians))]));
disp(sprintf('sind(%f)= %f\narcsind(%f)= %f',[angleDegrees sind(angleDegrees) sind(angleDegrees) asind(sind(angleDegrees))]));
disp('-----------------------');
disp(sprintf('cos(%f)= %f\nacos(%f)= %f',[angleRadians cos(angleRadians) cos(angleRadians) acos(cos(angleRadians))]));
disp(sprintf('cosd(%f)= %f\narccosd(%f)= %f',[angleDegrees cosd(angleDegrees) cosd(angleDegrees) acosd(cosd(angleDegrees))]));
disp('-----------------------');
disp(sprintf('tan(%f)= %f\natan(%f)= %f',[angleRadians tan(angleRadians) tan(angleRadians) atan(tan(angleRadians))]));
disp(sprintf('tand(%f)= %f\narctand(%f)= %f',[angleDegrees tand(angleDegrees) tand(angleDegrees) atand(tand(angleDegrees))]));
end
Output:
>> trigExample(78)
sin(1.361357)= 0.978148
asin(0.978148)= 1.361357
sind(78.000000)= 0.978148
arcsind(0.978148)= 78.000000
-----------------------
cos(1.361357)= 0.207912
acos(0.207912)= 1.361357
cosd(78.000000)= 0.207912
arccosd(0.207912)= 78.000000
-----------------------
tan(1.361357)= 4.704630
atan(4.704630)= 1.361357
tand(78.000000)= 4.704630
arctand(4.704630)= 78.000000

Maxima[edit]

a: %pi / 3;
[sin(a), cos(a), tan(a), sec(a), csc(a), cot(a)];
 
b: 1 / 2;
[asin(b), acos(b), atan(b), asec(1 / b), acsc(1 / b), acot(b)];
 
/* Hyperbolic functions are also available */
a: 1 / 2;
[sinh(a), cosh(a), tanh(a), sech(a), csch(a), coth(a)], numer;
[asinh(a), acosh(1 / a), atanh(a), asech(a), acsch(a), acoth(1 / a)], numer;

MAXScript[edit]

Maxscript trigonometric functions accept degrees only. The built-ins degToRad and radToDeg allow easy conversion.

local radians = pi / 4
local degrees = 45.0
 
--sine
print (sin (radToDeg radians))
print (sin degrees)
--cosine
print (cos (radToDeg radians))
print (cos degrees)
--tangent
print (tan (radToDeg radians))
print (tan degrees)
--arcsine
print (asin (sin (radToDeg radians)))
print (asin (sin degrees))
--arccosine
print (acos (cos (radToDeg radians)))
print (acos (cos degrees))
--arctangent
print (atan (tan (radToDeg radians)))
print (atan (tan degrees))

Metafont[edit]

Metafont has sind and cosd, which compute sine and cosine of an angle expressed in degree. We need to define the rest.

Pi := 3.14159;
vardef torad expr x = Pi*x/180 enddef;  % conversions
vardef todeg expr x = 180x/Pi enddef;
vardef sin expr x = sind(todeg(x)) enddef;  % radians version of sind
vardef cos expr x = cosd(todeg(x)) enddef;  % and cosd
 
vardef sign expr x = if x>=0: 1 else: -1 fi enddef; % commodity
 
vardef tand expr x =  % tan with arg in degree
if cosd(x) = 0:
infinity * sign(sind(x))
else: sind(x)/cosd(x) fi enddef;
vardef tan expr x = tand(todeg(x)) enddef; % arg in rad
 
% INVERSE
 
% the arc having x as tanget is that between x-axis and a line
% from the center to the point (1, x); MF angle says this
vardef atand expr x = angle(1,x) enddef;
vardef atan expr x = torad(atand(x)) enddef;  % rad version
 
% known formula to express asin and acos in function of
% atan; a+-+b stays for sqrt(a^2 - b^2) (defined in plain MF)
vardef asin expr x = 2atan(x/(1+(1+-+x))) enddef;
vardef acos expr x = 2atan((1+-+x)/(1+x)) enddef;
 
vardef asind expr x = todeg(asin(x)) enddef; % degree versions
vardef acosd expr x = todeg(acos(x)) enddef;
 
% commodity
def outcompare(expr a, b) = message decimal a & " = " & decimal b enddef;
 
% output tests
outcompare(torad(60), Pi/3);
outcompare(todeg(Pi/6), 30);
 
outcompare(Pi/3, asin(sind(60)));
outcompare(30, acosd(cos(Pi/6)));
outcompare(45, atand(tand(45)));
outcompare(Pi/4, atan(tand(45)));
 
outcompare(sin(Pi/3), sind(60));
outcompare(cos(Pi/4), cosd(45));
outcompare(tan(Pi/3), tand(60));
 
end

МК-61/52[edit]

sin	С/П	Вx	cos	С/П	Вx	tg	С/П	Вx	arcsin
С/П	Вx	arccos	С/П	Вx	arctg	С/П

Setting the units of angle (degrees, radians, grads) takes care of the switch Р-ГРД-Г.

NetRexx[edit]

/* NetRexx */
options replace format comments java crossref symbols nobinary utf8
 
numeric digits 30
 
parse 'Radians Degrees angle' RADIANS DEGREES ANGLE .;
parse 'sine cosine tangent arcsine arccosine arctangent' SINE COSINE TANGENT ARCSINE ARCCOSINE ARCTANGENT .
 
trigVals = ''
trigVals[RADIANS, ANGLE ] = (Rexx Math.PI) / 4 -- Pi/4 == 45 degrees
trigVals[DEGREES, ANGLE ] = 45.0
trigVals[RADIANS, SINE ] = (Rexx Math.sin(trigVals[RADIANS, ANGLE]))
trigVals[DEGREES, SINE ] = (Rexx Math.sin(Math.toRadians(trigVals[DEGREES, ANGLE])))
trigVals[RADIANS, COSINE ] = (Rexx Math.cos(trigVals[RADIANS, ANGLE]))
trigVals[DEGREES, COSINE ] = (Rexx Math.cos(Math.toRadians(trigVals[DEGREES, ANGLE])))
trigVals[RADIANS, TANGENT ] = (Rexx Math.tan(trigVals[RADIANS, ANGLE]))
trigVals[DEGREES, TANGENT ] = (Rexx Math.tan(Math.toRadians(trigVals[DEGREES, ANGLE])))
trigVals[RADIANS, ARCSINE ] = (Rexx Math.asin(trigVals[RADIANS, SINE]))
trigVals[DEGREES, ARCSINE ] = (Rexx Math.toDegrees(Math.acos(trigVals[DEGREES, SINE])))
trigVals[RADIANS, ARCCOSINE ] = (Rexx Math.acos(trigVals[RADIANS, COSINE]))
trigVals[DEGREES, ARCCOSINE ] = (Rexx Math.toDegrees(Math.acos(trigVals[DEGREES, COSINE])))
trigVals[RADIANS, ARCTANGENT] = (Rexx Math.atan(trigVals[RADIANS, TANGENT]))
trigVals[DEGREES, ARCTANGENT] = (Rexx Math.toDegrees(Math.atan(trigVals[DEGREES, TANGENT])))
 
say ' '.right(12)'|' RADIANS.right(17) '|' DEGREES.right(17) '|'
say ANGLE.right(12)'|' trigVals[RADIANS, ANGLE ].format(4, 12) '|' trigVals[DEGREES, ANGLE ].format(4, 12) '|'
say SINE.right(12)'|' trigVals[RADIANS, SINE ].format(4, 12) '|' trigVals[DEGREES, SINE ].format(4, 12) '|'
say COSINE.right(12)'|' trigVals[RADIANS, COSINE ].format(4, 12) '|' trigVals[DEGREES, COSINE ].format(4, 12) '|'
say TANGENT.right(12)'|' trigVals[RADIANS, TANGENT ].format(4, 12) '|' trigVals[DEGREES, TANGENT ].format(4, 12) '|'
say ARCSINE.right(12)'|' trigVals[RADIANS, ARCSINE ].format(4, 12) '|' trigVals[DEGREES, ARCSINE ].format(4, 12) '|'
say ARCCOSINE.right(12)'|' trigVals[RADIANS, ARCCOSINE ].format(4, 12) '|' trigVals[DEGREES, ARCCOSINE ].format(4, 12) '|'
say ARCTANGENT.right(12)'|' trigVals[RADIANS, ARCTANGENT].format(4, 12) '|' trigVals[DEGREES, ARCTANGENT].format(4, 12) '|'
say
 
return
 
Output:
            |           Radians |           Degrees |
       angle|    0.785398163397 |   45.000000000000 |
        sine|    0.707106781187 |    0.707106781187 |
      cosine|    0.707106781187 |    0.707106781187 |
     tangent|    1.000000000000 |    1.000000000000 |
     arcsine|    0.785398163397 |   45.000000000000 |
   arccosine|    0.785398163397 |   45.000000000000 |
  arctangent|    0.785398163397 |   45.000000000000 |

Nim[edit]

import math
 
proc radians(x): float = x * Pi / 180
proc degrees(x): float = x * 180 / Pi
 
let rad = Pi/4
let deg = 45.0
 
echo "Sine: ", sin(rad), " ", sin(radians(deg))
echo "Cosine : ", cos(rad), " ", cos(radians(deg))
echo "Tangent: ", tan(rad), " ", tan(radians(deg))
echo "Arcsine: ", arcsin(sin(rad)), " ", degrees(arcsin(sin(radians(deg))))
echo "Arccocose: ", arccos(cos(rad)), " ", degrees(arccos(cos(radians(deg))))
echo "Arctangent: ", arctan(tan(rad)), " ", degrees(arctan(tan(radians(deg))))

OCaml[edit]

OCaml's preloaded Pervasives module contains all six functions. The functions all accept radians only, so conversion is necessary when dealing with degrees.

let pi = 4. *. atan 1.
 
let radians = pi /. 4.
let degrees = 45.;;
 
Printf.printf "%f %f\n" (sin radians) (sin (degrees *. pi /. 180.));;
Printf.printf "%f %f\n" (cos radians) (cos (degrees *. pi /. 180.));;
Printf.printf "%f %f\n" (tan radians) (tan (degrees *. pi /. 180.));;
let arcsin = asin (sin radians);;
Printf.printf "%f %f\n" arcsin (arcsin *. 180. /. pi);;
let arccos = acos (cos radians);;
Printf.printf "%f %f\n" arccos (arccos *. 180. /. pi);;
let arctan = atan (tan radians);;
Printf.printf "%f %f\n" arctan (arctan *. 180. /. pi);;
Output:
0.707107 0.707107
0.707107 0.707107
1.000000 1.000000
0.785398 45.000000
0.785398 45.000000
0.785398 45.000000

Octave[edit]

function d = degree(rad)
d = 180*rad/pi;
endfunction
 
r = pi/3;
rd = degree(r);
 
funcs = { "sin", "cos", "tan", "sec", "cot", "csc" };
ifuncs = { "asin", "acos", "atan", "asec", "acot", "acsc" };
 
for i = 1 : numel(funcs)
v = arrayfun(funcs{i}, r);
vd = arrayfun(strcat(funcs{i}, "d"), rd);
iv = arrayfun(ifuncs{i}, v);
ivd = arrayfun(strcat(ifuncs{i}, "d"), vd);
printf("%s(%f) = %s(%f) = %f (%f)\n",
funcs{i}, r, strcat(funcs{i}, "d"), rd, v, vd);
printf("%s(%f) = %f\n%s(%f) = %f\n",
ifuncs{i}, v, iv,
strcat(ifuncs{i}, "d"), vd, ivd);
endfor
Output:
sin(1.047198) = sind(60.000000) = 0.866025 (0.866025)
asin(0.866025) = 1.047198
asind(0.866025) = 60.000000
cos(1.047198) = cosd(60.000000) = 0.500000 (0.500000)
acos(0.500000) = 1.047198
acosd(0.500000) = 60.000000
tan(1.047198) = tand(60.000000) = 1.732051 (1.732051)
atan(1.732051) = 1.047198
atand(1.732051) = 60.000000
sec(1.047198) = secd(60.000000) = 2.000000 (2.000000)
asec(2.000000) = 1.047198
asecd(2.000000) = 60.000000
cot(1.047198) = cotd(60.000000) = 0.577350 (0.577350)
acot(0.577350) = 1.047198
acotd(0.577350) = 60.000000
csc(1.047198) = cscd(60.000000) = 1.154701 (1.154701)
acsc(1.154701) = 1.047198
acscd(1.154701) = 60.000000

(Lacking in this code but present in GNU Octave: sinh, cosh, tanh, coth and inverses)


Oforth[edit]

import: math
 
: testTrigo
| rad deg hyp z |
Pi 4 / ->rad
45.0 ->deg
0.5 ->hyp
 
System.Out rad sin << " - " << deg asRadian sin << cr
System.Out rad cos << " - " << deg asRadian cos << cr
System.Out rad tan << " - " << deg asRadian tan << cr
 
printcr
 
rad sin asin ->z
System.Out z << " - " << z asDegree << cr
 
rad cos acos ->z
System.Out z << " - " << z asDegree << cr
 
rad tan atan ->z
System.Out z << " - " << z asDegree << cr
 
printcr
 
System.Out hyp sinh << " - " << hyp sinh asinh << cr
System.Out hyp cosh << " - " << hyp cosh acosh << cr
System.Out hyp tanh << " - " << hyp tanh atanh << cr ;
Output:
0.707106781186547 - 0.707106781186547
0.707106781186548 - 0.707106781186548
1 - 1

0.785398163397448 - 45
0.785398163397448 - 45
0.785398163397448 - 45

0.521095305493747 - 0.5
1.12762596520638 - 0.5
0.46211715726001 - 0.5

ooRexx[edit]

rxm.cls                                                    20 March 2014

The distribution of ooRexx contains a function package called rxMath
that provides the computation of trigonometric and some other functions.
Based on the underlying C-library the precision of the returned values
is limited to 16 digits. Close observation show that sometimes the last
one to three digits of the returned values are not correct.
Many years ago I experimented with implementing these functions in Rexx
with its virtually unlimited precision.
The rxm class is intended to provide the same functionality as rxMath
with no limit on the specified or implied precision.

Functions in class rxm and invocation syntax are the same as
in the rxMath library. They are implemented as routines which
perform the checking of argument values and invoke the corresponding
methods. Here is a list of the supported functions and a concise
syntax specification.

The arguments are represented by these letters:

x is the value for which the respective function must be evaluated.
b and c for RxCalcPower are base and exponent, respectively.

p if specified is the desired precision (number of digits) in the result.
  It can be any integer from 1 to 999999.
  See below for the default used.

u if specified, is the unit of x given to the trigonometric functions
  or the unit of the value returned by the Arcus functions.
  It can be 'R', 'D', or 'G' for radians, degrees, or grades, respectively.
  See below for the default used.

Trigonometric functions:

• rxmCos(x[,[p][,u]])
• rxmCotan(x[,[p][,u]])
• rxmSin(x[,[p][,u]])
• rxmTan(x[,[p][,u]])

Arcus functions:

• rxmArcCos(x[,[p][,u]])
• rxmArcSin(x[,[p][,u]])
• rxmArcTan(x[,[p][,u]])

Hyperbolic functions:

• rxmCosH(x[,p])
• rxmSinH(x[,p])
• rxmTanH(x[,p])

• rxmExp(x[,p])      e**x
• rxmLog(x[,p])      Natural logarithm of x
• rxmLog10(x[,p])    Brigg's logarithm of x
• rxmSqrt(x[,p])     Square root of x

• rxmPower(b,c[,p])  b**c

• rxmPi([p])         pi to the specified or default precision

Values used for p and u if these are omitted in the invocation
==============================================================

The directive ::REQUIRES rxm.cls creates an instance of the class
  .local~my.rxm=.rxm~new(16,"D")
which sets the defaults for p=16 and u='D'.
These are used when p or u are omitted in a function invocation.
They can be changed by changing the respective class attributes as follows:
  .locaL~my.rxm~precision=50
  .locaL~my.rxm~type='R'
The current setting of these attributes can be retrieved as follows:
  .locaL~my.rxm~precision()
  .locaL~my.rxm~type()

While I tried to get full compatibility there remain a few
(actually very few) differences:

  rxCalcTan(90) raises the Syntax condition (will be fixed in the next ooRexx release)
  rxCalcexp(x) limits x to 709. or so and returns '+infinity' for larger exponents
/* REXX ---------------------------------------------------------------
* show how the functions can be used
* 03.05.2014 Walter Pachl
*--------------------------------------------------------------------*/

Say 'Default precision:' .locaL~my.rxm~precision()
Say 'Default type: ' .locaL~my.rxm~type()
Say 'rxmsin(60) ='rxmsin(60) -- use default precision and type
Say 'rxmsin(1,21,"R")='rxmsin(1,21,'R') -- precision and type specified
Say 'rxmlog(-1) ='rxmlog(-1)
Say 'rxmlog( 0) ='rxmlog( 0)
Say 'rxmlog( 1) ='rxmlog( 1)
Say 'rxmlog( 2) ='rxmlog( 2)
.locaL~my.rxm~precision=50
.locaL~my.rxm~type='R'
Say 'Changed precision:' .locaL~my.rxm~precision()
Say 'Changed type: ' .locaL~my.rxm~type()
Say 'rxmsin(1) ='rxmsin(1) -- use changed precision and type
::requires rxm.cls
Output:
Default precision: 16
Default type:      D
rxmsin(60)      =0.8660254037844386
rxmsin(1,21,"R")=0.841470984807896506653
rxmlog(-1)      =nan
rxmlog( 0)      =-infinity
rxmlog( 1)      =0
rxmlog( 2)      =0.6931471805599453
Changed precision: 50
Changed type:      R
rxmsin(1)       =0.84147098480789650665250232163029899962256306079837
/********************************************************************
* Package rxm
* implements the functions available in RxMath with high precision
* by computing the values with significantly increased precision
* and rounding the result to the specified precision.
* This started 10 years ago when Vladimir Zabrodsky published his
* Album of Algorithms http://dhost.info/zabrodskyvlada/aat/
* Gerard Schildberger suggests on rosettacode.org to use +10 digits
* Rony Flatscher suggested and helped to turn this into an ooRexx class
* Rick McGuire advised on using Use STRICT Arg for argument checking
* Alexander Seik creates this documentation
* Horst Wegscheider helped with reviewing and some improvements
* 12.04.2014 Walter Pachl
* Documentation: see rxmath.pdf in the ooRexx distribution
* and rxm.doc (here)
* 13.04.2014 WP arcsin and arctan commentary corrected (courtesy Horst)
* 13.04.2014 WP improve arctan performance
* 20.04.2014 WP towards completion
* 24.04.2014 WP arcsin verbessert. courtesy Horst Wegscheider
* 28.04.2014 WP run ooRexxDoc
* 11.08.2014 WP replace log algorithm with Vladimir Zabrodsky's code
**********************************************************************/

.local~my.rxm=.rxm~new(16,"D")
 
::Class rxm Public
 
::Method init
Expose precision type
Use Arg precision=(digits()),type='D'
 
::attribute precision set
Expose precision
Use Strict Arg precision=(digits())
 
::attribute precision get
 
::attribute type set
Expose type
Use Strict Arg type='R'
 
::attribute type get
 
::Method arccos
/***********************************************************************
* Return arccos(x,precision,type) -- with specified precision
* arccos(x) = pi/2 - arcsin(x)
***********************************************************************/

Expose precision type
Use Strict Arg x,xprec=(precision),xtype=(type)
iprec=xprec+10
Numeric Digits iprec
If x=1 Then
r=0
Else Do
r=self~arcsin(x,iprec,'R')
If r='nan' Then
Return r
r=self~pi(iprec)/2 - r
End
Select
When xtype='D' Then
r=r*180/self~pi(iprec)
When xtype='G' Then
r=r*200/self~pi(iprec)
Otherwise
Nop
End
Numeric Digits xprec
Return (r+0)
 
::Method arcsin
/***********************************************************************
* Return arcsin(x,precision,type) -- with specified precision
* arcsin(x) = x+(x**3)*1/2*3+(x**5)*1*3/2*4*5+(x**7)*1*3*5/2*4*6*7+...
***********************************************************************/

Expose precision type
Use Strict Arg x,xprec=(precision),xtype=(type)
iprec=xprec+10
Numeric Digits iprec
sign=sign(x)
If x<0 Then
x=abs(x)
Select
When abs(x)>1 Then
Return 'nan'
When x=0 Then
r=0
When x=1 Then
r=rxmpi(iprec)/2
When x<0.8 Then Do
o=x
u=1
r=x
Do i=3 By 2 Until ra=r
ra=r
o=o*x*x*(i-2)
u=u*(i-1)*i/(i-2)
r=r+(o/u)
If r=ra Then
r=r+(o/u)/2 /* final touch */
End
End
Otherwise Do
z=x
r=x
o=x
s=x*x
do j=2 by 2;
o=o*s*(j-1)/j;
z=z+o/(j+1);
if z=r then
leave
r=z;
end
/***********************
y=(1-x*x)/4
n=0.5-self~sqrt(y,iprec)
z=self~sqrt(n,iprec)
r=2*self~arcsin(z,xprec)
***********************/

End
End
Select
When xtype='D' Then
r=r*180/self~pi(iprec)
When xtype='G' Then
r=r*200/self~pi(iprec)
Otherwise
Nop
End
Numeric Digits xprec
Return sign*(r+0)
 
::Method arctan
/***********************************************************************
* Return arctan(x,precision,type) -- with specified precision
* x=0 -> arctan(x) = 0
* If x>0 Then
* x<1 -> arctan(x) = arcsin(x/sqrt(x**2+1))
* x=1 -> arctan(x) = pi/4
* x>1 -> arctan(x) = pi/2-arcsin((1/x)/sqrt((1/x)**2+1))
* Else
* adjust as necessary
***********************************************************************/

Expose precision type
Use Strict Arg x,xprec=(precision),xtype=(type)
iprec=xprec+10
Numeric Digits iprec
Select
When abs(x)<1 Then
r=self~arcsin(x/self~sqrt(1+x**2,iprec),iprec,'R')
When abs(x)=1 Then
r=self~pi(iprec)/4*sign(x)
Otherwise Do
xr=1/abs(x)
r=self~arcsin(xr/self~sqrt(1+xr**2,iprec),iprec,'R')
If x>0 Then
r=self~pi(iprec)/2-r
Else
r=-self~pi(iprec)/2+r
End
End
Select
When xtype='D' Then
r=r*180/self~pi(iprec)
When xtype='G' Then
r=r*200/self~pi(iprec)
Otherwise
Nop
End
Numeric Digits xprec
Return (r+0)
 
::Method arsinh
/***********************************************************************
* Return arsinh(x,precision,type) -- with specified precision
* arsinh(x) = ln(x+sqrt(x**2+1))
***********************************************************************/

Expose precision
Use Strict Arg x,xprec=(precision)
iprec=xprec+10
Numeric Digits iprec
x2p1=x**2+1
r=self~log(x+self~sqrt(x2p1,iprec),iprec)
Numeric Digits xprec
Return (r+0)
 
::Method cos
/* REXX *************************************************************
* Return cos(x,precision,type) -- with the specified precision
* cos(x)=sin(x+pi/2)
********************************************************************/

Expose precision type
Use Strict Arg x,xprec=(precision),xtype=(type)
iprec=xprec+10
Numeric Digits iprec
Select
When xtype='R' Then xa=x+self~pi(iprec)/2
When xtype='D' Then xa=x+90
When xtype='G' Then xa=x+100
End
r=self~sin(xa,iprec,xtype)
Numeric Digits xprec
Return (r+0)
 
::Method cosh
/* REXX ****************************************************************
* Return cosh(x,precision,type) -- with specified precision
* cosh(x) = 1+(x**2/2!)+(x**4/4!)+(x**6/6!)+-...
***********************************************************************/

Expose precision
Use Strict Arg x,xprec=(precision)
iprec=xprec+10
Numeric Digits iprec
o=1
u=1
r=1
Do i=2 By 2 Until ra=r
ra=r
o=o*x*x
u=u*i*(i-1)
r=r+(o/u)
End
Numeric Digits xprec
Return (r+0)
 
::Method cotan
/* REXX *************************************************************
* Return cotan(x,precision,type) -- with the specified precision
* cot(x)=cos(x)/sin(x)
********************************************************************/

Expose precision type
Use Strict Arg x,xprec=(precision),xtype=(type)
iprec=xprec+10
Numeric Digits iprec
s=self~sin(x,iprec,xtype)
c=self~cos(x,iprec,xtype)
If s=0 Then
Return '+infinity'
r=c/s
Numeric Digits xprec
Return (r+0)
 
::Method exp
/***********************************************************************
* exp(x,precision) returns e**x -- with specified precision
* exp(x,precision,base) returns base**x -- with specified precision
***********************************************************************/

Expose precision
Use Strict Arg x,xprec=(precision),xbase=''
iprec=xprec+10
Numeric Digits iprec
Numeric Fuzz 3
If xbase<>'' Then Do
Select
When xbase=0 Then Do
Select
When x<0 Then Return '+infinity'
When x=0 Then Return 'nan'
Otherwise Return 0
End
End
When xbase=1 Then Return 1
When xbase<0 Then Do
Select
When x=0 Then Return 1
When datatype(x,'W')=0 Then Return 'nan'
Otherwise Do
r=xbase**x
Numeric Digits xprec
Return r+0
End
End
End
Otherwise
x=x*self~log(xbase,iprec)
End
End
o=1
u=1
r=1
Do i=1 By 1 Until ra=r
ra=r
o=o*x
u=u*i
r=r+(o/u)
End
Numeric Digits xprec
Return (r+0)
 
::Method log
/***********************************************************************
* log(x,precision) -- returns ln(x) with specified precision
* log(x,precision,base) -- returns blog(x) with specified precision
* Three different series are used for ln(x): x in range 0 to 0.5
* 0.5 to 1.5
* 1.5 to infinity
***********************************************************************/

Expose precision
Use Strict Arg x,xprec=(precision),xbase=''
iprec=xprec+100
Numeric Digits iprec
Select
When x=0 Then Return '-infinity'
When x<0 Then Return 'nan'
When x<1 Then r= -self~Log(1/X,xprec)
Otherwise Do
do M = 0 until (2 ** M) > X; end
M = M - 1
Z = X / (2 ** M)
Zeta = (1 - Z) / (1 + Z)
N = Zeta; Ln = Zeta; Zetasup2 = Zeta * Zeta
do J = 1
N = N * Zetasup2; NewLn = Ln + N / (2 * J + 1)
if NewLn = Ln then Do
r= M * self~LN2P(xprec) - 2 * Ln
Leave
End
Ln = NewLn
end
End
End
If x>0 Then Do
If xbase>'' Then
r=r/self~log(xbase,iprec)
Numeric Digits xprec
r=r+0
End
Return r
 
::Method ln2p
Parse Arg p
Numeric Digits p+10
If p<=1000 Then
Return self~ln2()
n=1/3
ln=n
zetasup2=1/9
Do j=1
n=n*zetasup2
newln=ln+n/(2*j+1)
If newln=ln Then
Return 2*ln
ln=newln
End
 
::Method LN2
V = ''
V = V || 0.69314718055994530941723212145817656807
V = V || 5500134360255254120680009493393621969694
V = V || 7156058633269964186875420014810205706857
V = V || 3368552023575813055703267075163507596193
V = V || 0727570828371435190307038623891673471123350
v=''
v=v||0.69314718055994530941723212145817656807
v=v||5500134360255254120680009493393621969694
v=v||7156058633269964186875420014810205706857
v=v||3368552023575813055703267075163507596193
v=v||0727570828371435190307038623891673471123
v=v||3501153644979552391204751726815749320651
v=v||5552473413952588295045300709532636664265
v=v||4104239157814952043740430385500801944170
v=v||6416715186447128399681717845469570262716
v=v||3106454615025720740248163777338963855069
v=v||5260668341137273873722928956493547025762
v=v||6520988596932019650585547647033067936544
v=v||3254763274495125040606943814710468994650
v=v||6220167720424524529612687946546193165174
v=v||6813926725041038025462596568691441928716
v=v||0829380317271436778265487756648508567407
v=v||7648451464439940461422603193096735402574
v=v||4460703080960850474866385231381816767514
v=v||3866747664789088143714198549423151997354
v=v||8803751658612753529166100071053558249879
v=v||4147295092931138971559982056543928717000
v=v||7218085761025236889213244971389320378439
v=v||3530887748259701715591070882368362758984
v=v||2589185353024363421436706118923678919237
v=v||231467232172053401649256872747782344535348
 
return V
 
::Method log10
/***********************************************************************
* Return log10(x,prec) specified precision
***********************************************************************/

Expose precision
Use Strict Arg x,xprec=(precision)
iprec=xprec+10
r=self~log(x,iprec,10)
Numeric Digits xprec
Return (r+0)
 
::Method pi
/* REXX *************************************************************
* Return pi with the specified precision
********************************************************************/

Expose precision
Use Strict Arg xprec=(precision)
p='3.141592653589793238462643383279502884197169399375'||,
'10582097494459230781640628620899862803482534211706'||,
'79821480865132823066470938446095505822317253594081'||,
'28481117450284102701938521105559644622948954930381'||,
'96442881097566593344612847564823378678316527120190'||,
'91456485669234603486104543266482133936072602491412'||,
'73724587006606315588174881520920962829254091715364'||,
'36789259036001133053054882046652138414695194151160'||,
'94330572703657595919530921861173819326117931051185'||,
'48074462379962749567351885752724891227938183011949'||,
'12983367336244065664308602139494639522473719070217'||,
'98609437027705392171762931767523846748184676694051'||,
'32000568127145263560827785771342757789609173637178'||,
'72146844090122495343014654958537105079227968925892'||,
'35420199561121290219608640344181598136297747713099'||,
'60518707211349999998372978049951059731732816096318'||,
'59502445945534690830264252230825334468503526193118'||,
'81710100031378387528865875332083814206171776691473'||,
'03598253490428755468731159562863882353787593751957'||,
'781857780532171226806613001927876611195909216420199'
If xprec>1000 Then Do /* more than 1000 digits wanted */
iprec=xprec+10 /* internal precision */
Numeric Digits iprec
new=1
a=sqrt(2,iprec)
b=0
p=2+a
Do i=1 By 1 Until p=pi
pi=p
y=self~sqrt(a,iprec)
a1=(y+1/y)/2
b1=y*(b+1)/(b+a)
p=pi*b1*(1+a1)/(1+b1)
a=a1
b=b1
End
End
Numeric Digits xprec
Return (p+0)
 
::Method power
/***********************************************************************
* power(base,exponent,precision) returns base**exponent
* -- with specified precision
***********************************************************************/

Expose precision
Use Strict Arg b,c,xprec=(precision)
Numeric Digits xprec
rsign=1
If b<0 Then Do /* negative base */
If datatype(c,'W') Then Do /* Exponent is an integer */
If c//2=1 Then /* .. an odd number */
rsign=-1 /* Resuld will be negative */
b=abs(b) /* proceed with positive base */
End
Else Do /* Exponent is not an integer */
-- Say 'for a negative base ('||b')',
'exponent ('c') must be an integer'
Return 'nan' /* Return not a number */
End
End
If c=0 Then Do
If b>=0 Then
r=1
End
Else
r=self~exp(c,xprec,b)
If datatype(r)<>'NUM' Then
Return r
Return rsign*r
 
::Method sqrt
/* REXX *************************************************************
* Return sqrt(x,precision) -- with the specified precision
********************************************************************/

Expose precision type
Use Strict Arg x,xprec=(precision)
If x<0 Then Do
Return 'nan'
End
iprec=xprec+10
Numeric Digits iprec
r0= x
r = 1
Do i=1 By 1 Until r=r0 | (abs(r*r-x)<10**-iprec)
r0 = r
r = (r + x/r) / 2
End
Numeric Digits xprec
Return (r+0)
 
::Method sin
/* REXX *************************************************************
* Return sin(x,precision,type) -- with the specified precision
* xtype = 'R' (radians, default) 'D' (degrees) 'G' (grades)
* sin(x) = x-(x**3/3!)+(x**5/5!)-(x**7/7!)+-...
********************************************************************/

Expose precision type
Use Strict Arg x,xprec=(precision),xtype=(type)
iprec=xprec+10 /* internal precision */
Numeric Digits iprec
/* first use pi constant or compute it if necessary */
pi=self~pi(iprec)
/* normalize x to be between 0 and 2*pi (or equivalent) */
/* and convert degrees or grades to radians */
xx=x
Select
When xtype='R' Then Do
Do While xx>=pi*2; xx=xx-pi*2; End
Do While xx<0; xx=xx+pi*2; End
End
When xtype='D' Then Do
Do While xx>=360; xx=xx-360; End
Do While xx<0; xx=xx+360; End
xx=xx*pi/180
End
When xtype='G' Then Do
Do While xx>=400; xx=xx-400; End
Do While xx<0; xx=xx+400; End
xx=xx*pi/200
End
End
/* normalize xx to be between 0 and pi/2 */
sign=1
Select
When xx<=pi/2 Then Nop
When xx<=pi Then xx=pi-xx
When xx<=3*pi/2 Then Do; sign=-1; xx=xx-pi; End
Otherwise Do; sign=-1; xx=2*pi-xx; End
End
/* now compute the Taylor series for the normalized xx */
o=xx
u=1
r=xx
If abs(xx)<10**(-iprec) Then
r=0
Else Do
Do i=3 By 2 Until ra=r
ra=r
o=-o*xx*xx
u=u*i*(i-1)
r=r+(o/u)
End
End
Numeric Digits xprec
Return sign*(r+0)
 
::Method sinh
/* REXX ****************************************************************
* Return sinh(x,precision) -- with specified precision
* sinh(x) = x+(x**3/3!)+(x**5/5!)+(x**7/7!)+-...
* 920903 Walter Pachl
***********************************************************************/

Expose precision
Use Strict Arg x,xprec=(precision)
iprec=xprec+10
Numeric Digits iprec
o=x
u=1
r=x
Do i=3 By 2 Until ra=r
ra=r
o=o*x*x
u=u*i*(i-1)
r=r+(o/u)
End
Numeric Digits xprec
Return (r+0)
 
::Method tan
/* REXX *************************************************************
* Return tan(x,precision,type) -- with the specified precision
* tan(x)=sin(x)/cos(x)
********************************************************************/

Expose precision type
Use Strict Arg x,xprec=(precision),xtype=(type)
iprec=xprec+10
Numeric Digits iprec
s=self~sin(x,iprec,xtype)
c=self~cos(x,iprec,xtype)
If c=0 Then
Return '+infinity'
t=s/c
Numeric Digits xprec
Return (t+0)
 
::Method tanh
/***********************************************************************
* Return tanh(x,precision) -- with specified precision
* tanh(x) = sinh(x)/cosh(x)
***********************************************************************/

Expose precision
Use Strict Arg x,xprec=(precision)
iprec=xprec+10
Numeric Digits iprec
r=self~sinh(x,iprec)/self~cosh(x,iprec)
Numeric Digits xprec
Return (r+0)
 
::routine rxmarccos public
Use Strict Arg x,xprec=(.my.rxm~precision),xtype=(.my.rxm~type)
 
If datatype(x,'NUM')=0 Then Do
-- Say 'Argument 1 must be a number'
Raise Syntax 88.902 array(1,x)
End
 
If datatype(xprec,'W')=0 Then Do
-- Say 'Argument 2 must be a positive whole number'
Raise Syntax 88.905 array(2,xprec)
End
 
If xprec<1 | 999999<xprec Then Do
-- Say 'Argument 2 must be a whole number between 1 and 999999'
Raise Syntax 88.907 array(2,1,999999,xprec)
End
 
If x<-1 | 1<x Then
Return 'nan'
 
return .my.rxm~arccos(x,xprec,xtype)
 
::routine rxmarcsin public
Use Strict Arg x,xprec=(.my.rxm~precision),xtype=(.my.rxm~type)
 
If datatype(x,'NUM')=0 Then Do
-- Say 'Argument 1 must be a number'
Raise Syntax 88.902 array(1,x)
End
 
If datatype(xprec,'W')=0 Then Do
-- Say 'Argument 2 must be a positive whole number'
Raise Syntax 88.905 array(2,xprec)
End
 
If xprec<1 | 999999<xprec Then Do
-- Say 'Argument 2 must be a whole number between 1 and 999999'
Raise Syntax 88.907 array(2,1,999999,xprec)
End
 
If wordpos(xtype,'R D G')=0 Then Do
-- Say 'Argument 3 must be R, D, or G'
Raise Syntax 88.907 array(3,'R, D, or G',xtype)
End
 
If x<-1 | 1<x Then
Return 'nan'
 
return .my.rxm~arcsin(x,xprec,xtype)
 
::routine rxmarctan public
Use Strict Arg x,xprec=(.my.rxm~precision),xtype=(.my.rxm~type)
 
If datatype(x,'NUM')=0 Then Do
-- Say 'Argument 1 must be a number'
Raise Syntax 88.902 array(1,x)
End
 
If datatype(xprec,'W')=0 Then Do
-- Say 'Argument 2 must be a positive whole number'
Raise Syntax 88.905 array(2,xprec)
End
 
If xprec<1 | 999999<xprec Then Do
-- Say 'Argument 2 must be a whole number between 1 and 999999'
Raise Syntax 88.907 array(2,1,999999,xprec)
End
 
If wordpos(xtype,'R D G')=0 Then Do
-- Say 'Argument 3 must be R, D, or G'
Raise Syntax 88.907 array(3,'R, D, or G',xtype)
End
 
return .my.rxm~arctan(x,xprec,xtype)
 
::routine rxmarsinh public
Use Strict Arg x,xprec=(.my.rxm~precision)
 
If datatype(x,'NUM')=0 Then Do
-- Say 'Argument 1 must be a number'
Raise Syntax 88.902 array(1,x)
End
 
If datatype(xprec,'W')=0 Then Do
-- Say 'Argument 2 must be a positive whole number'
Raise Syntax 88.905 array(2,xprec)
End
 
If xprec<1 | 999999<xprec Then Do
-- Say 'Argument 2 must be a whole number between 1 and 999999'
Raise Syntax 88.907 array(2,1,999999,xprec)
End
 
return .my.rxm~arsinh(x,xprec)
 
::routine rxmcos public
Use Strict Arg x,xprec=(.my.rxm~precision),xtype=(.my.rxm~type)
 
If datatype(x,'NUM')=0 Then Do
-- Say 'Argument 1 must be a number'
Raise Syntax 88.902 array(1,x)
End
 
If datatype(xprec,'W')=0 Then Do
-- Say 'Argument 2 must be a positive whole number'
Raise Syntax 88.905 array(2,xprec)
End
 
If xprec<1 | 999999<xprec Then Do
-- Say 'Argument 2 must be a whole number between 1 and 999999'
Raise Syntax 88.907 array(2,1,999999,xprec)
End
 
If wordpos(xtype,'R D G')=0 Then Do
-- Say 'Argument 3 must be R, D, or G'
Raise Syntax 88.907 array(3,'R, D, or G',xtype)
End
 
return .my.rxm~cos(x,xprec,xtype)
 
::routine rxmcosh public
Use Strict Arg x,xprec=(.my.rxm~precision)
 
If datatype(x,'NUM')=0 Then Do
-- Say 'Argument 1 must be a number'
Raise Syntax 88.902 array(1,x)
End
 
If datatype(xprec,'W')=0 Then Do
-- Say 'Argument 2 must be a positive whole number'
Raise Syntax 88.905 array(2,xprec)
End
 
If xprec<1 | 999999<xprec Then Do
-- Say 'Argument 2 must be a whole number between 1 and 999999'
Raise Syntax 88.907 array(2,1,999999,xprec)
End
 
return .my.rxm~cosh(x,xprec)
 
::routine rxmcotan public
Use Strict Arg x,xprec=(.my.rxm~precision),xtype=(.my.rxm~type)
 
If datatype(x,'NUM')=0 Then Do
-- Say 'Argument 1 must be a number'
Raise Syntax 88.902 array(1,x)
End
 
If datatype(xprec,'W')=0 Then Do
-- Say 'Argument 2 must be a positive whole number'
Raise Syntax 88.905 array(2,xprec)
End
 
If xprec<1 | 999999<xprec Then Do
-- Say 'Argument 2 must be a whole number between 1 and 999999'
Raise Syntax 88.907 array(2,1,999999,xprec)
End
 
If wordpos(xtype,'R D G')=0 Then Do
-- Say 'Argument 3 must be R, D, or G'
Raise Syntax 88.907 array(3,'R, D, or G',xtype)
End
 
return .my.rxm~cotan(x,xprec)
 
::routine rxmexp public
Use Strict Arg x,xprec=(.my.rxm~precision),xbase=''
If datatype(x,'NUM')=0 Then Do
-- Say 'Argument 1 must be a number'
Raise Syntax 88.902 array(1,x)
End
 
If datatype(xprec,'W')=0 Then Do
-- Say 'Argument 2 must be a whole number between 1 and 999999'
Raise Syntax 88.905 array(2,xprec)
End
 
If xprec<1 | 999999<xprec Then Do
-- Say 'Argument 2 must be a whole number between 1 and 999999'
Raise Syntax 88.907 array(2,1,999999,xprec)
End
 
If datatype(xbase,'NUM')=0 & xbase<>'' Then Do
-- Say 'Argument 3 must be omitted or a number'
Raise Syntax 88.902 array(3,xbase)
End
 
Select
When x<0 Then Do
iprec=xprec+10
Numeric Digits iprec
z=.my.rxm~exp(abs(x),iprec,xbase)
Select
When z=0 Then Return '+infinity'
When datatype(z)<>'NUM' Then Return z
Otherwise r=1/z
End
Numeric Digits xprec
return r+0
End
When x=0 Then Do
If xbase=0 Then
Return 'nan'
Else
Return 1
End
Otherwise
return .my.rxm~exp(x,xprec,xbase)
End
 
::routine rxmlog public
Use Strict Arg x,xprec=(.my.rxm~precision),xbase=''
 
If datatype(x,'NUM')=0 Then Do
-- Say 'Argument 1 must be a number'
Raise Syntax 88.902 array(1,x)
End
 
If datatype(xprec,'W')=0 Then Do
-- Say 'Argument 2 must be a whole number between 1 and 999999'
Raise Syntax 88.905 array(2,xprec)
End
 
If xprec<1 | 999999<xprec Then Do
-- Say 'Argument 2 must be a whole number between 1 and 999999'
Raise Syntax 88.907 array(2,1,999999,xprec)
End
 
If xbase<>'' &,
datatype(xbase,'NUM')=0 Then Do
-- Say 'Argument 3 must be a number'
Raise Syntax 88.902 array(3,xbase)
End
 
If x=0 Then
Return '-infinity'
 
If x<0 Then
Return 'nan'
 
return .my.rxm~log(x,xprec,xbase)
 
::routine rxmlog10 public
Use Strict Arg x,xprec=(.my.rxm~precision)
 
If datatype(x,'NUM')=0 Then Do
-- Say 'Argument 1 must be a number'
Raise Syntax 88.902 array(1,x)
End
 
If datatype(xprec,'W')=0 Then Do
-- Say 'Argument 2 must be a whole number between 1 and 999999'
Raise Syntax 88.905 array(2,xprec)
End
 
If xprec<1 | 999999<xprec Then Do
-- Say 'Argument 2 must be a whole number between 1 and 999999'
Raise Syntax 88.907 array(2,1,999999,xprec)
End
 
If x=0 Then
Return '-infinity'
 
If x<0 Then
Return 'nan'
 
return .my.rxm~log10(x,xprec)
 
::routine rxmpi public
Use Strict Arg xprec=(.my.rxm~precision)
 
If datatype(xprec,'W')=0 Then Do
-- Say 'Argument 2 must be a whole number between 1 and 999999'
Raise Syntax 88.905 array(2,xprec)
End
 
If xprec<1 | 999999<xprec Then Do
-- Say 'Argument 2 must be a whole number between 1 and 999999'
Raise Syntax 88.907 array(2,1,999999,xprec)
End
 
return .my.rxm~pi(xprec)
 
::routine rxmpower public
Use Strict Arg b,e,xprec=(.my.rxm~precision)
 
If datatype(b,'NUM')=0 Then Do
-- Say 'Argument 1 must be a number'
Raise Syntax 88.902 array(1,b)
End
 
If datatype(e,'NUM')=0 Then Do
-- Say 'Argument 2 must be a number'
Raise Syntax 88.902 array(2,e)
End
 
If datatype(xprec,'W')=0 Then Do
-- Say 'Argument 3 must be a whole number between 1 and 999999'
Raise Syntax 88.905 array(2,xprec)
End
 
If xprec<1 | 999999<xprec Then Do
-- Say 'Argument 3 must be a whole number between 1 and 999999'
Raise Syntax 88.907 array(3,1,999999,xprec)
End
 
If b<0 & datatype(e,'W')=0 Then
Return 'nan'
 
return .my.rxm~power(b,e,xprec)
 
::routine rxmsqrt public
Use Strict Arg x,xprec=(.my.rxm~precision)
 
If datatype(x,'NUM')=0 Then Do
-- Say 'Argument 1 must be a number'
Raise Syntax 88.902 array(1,x)
End
 
If datatype(xprec,'W')=0 Then Do
-- Say 'Argument 2 must be a whole number between 1 and 999999'
Raise Syntax 88.905 array(2,xprec)
End
 
If xprec<1 | 999999<xprec Then Do
-- Say 'Argument 2 must be a whole number between 1 and 999999'
Raise Syntax 88.907 array(2,1,999999,xprec)
End
Select
When x<0 Then Return 'nan'
When x=0 Then Return 0
Otherwise
return .my.rxm~sqrt(x,xprec)
End
 
::routine rxmsin public
Use Strict Arg x,xprec=(.my.rxm~precision),xtype=(.my.rxm~type)
 
If datatype(x,'NUM')=0 Then Do
-- Say 'Argument 1 must be a number'
Raise Syntax 88.902 array(1,x)
End
 
If datatype(xprec,'W')=0 Then Do
-- Say 'Argument 2 must be a positive whole number'
Raise Syntax 88.905 array(2,xprec)
End
 
If xprec<1 | 999999<xprec Then Do
-- Say 'Argument 2 must be a whole number between 1 and 999999'
Raise Syntax 88.907 array(2,1,999999,xprec)
End
 
If wordpos(xtype,'R D G')=0 Then Do
-- Say 'Argument 3 must be R, D, or G'
Raise Syntax 88.907 array(3,'R, D, or G',xtype)
End
 
return .my.rxm~sin(x,xprec,xtype)
 
::routine rxmsinh public
Use Strict Arg x,xprec=(.my.rxm~precision)
 
If datatype(x,'NUM')=0 Then Do
-- Say 'Argument 1 must be a number'
Raise Syntax 88.902 array(1,x)
End
 
If datatype(xprec,'W')=0 Then Do
-- Say 'Argument 2 must be a positive whole number'
Raise Syntax 88.905 array(2,xprec)
End
 
If xprec<1 | 999999<xprec Then Do
-- Say 'Argument 2 must be a whole number between 1 and 999999'
Raise Syntax 88.907 array(2,1,999999,xprec)
End
 
return .my.rxm~sinh(x,xprec)
 
::routine rxmtan public
Use Strict Arg x,xprec=(.my.rxm~precision),xtype=(.my.rxm~type)
 
If datatype(x,'NUM')=0 Then Do
-- Say 'Argument 1 must be a number'
Raise Syntax 88.902 array(1,x)
End
 
If datatype(xprec,'W')=0 Then Do
-- Say 'Argument 2 must be a positive whole number'
Raise Syntax 88.905 array(2,xprec)
End
 
If xprec<1 | 999999<xprec Then Do
-- Say 'Argument 2 must be a whole number between 1 and 999999'
Raise Syntax 88.907 array(2,1,999999,xprec)
End
 
If wordpos(xtype,'R D G')=0 Then Do
-- Say 'Argument 3 must be R, D, or G'
Raise Syntax 88.907 array(3,'R, D, or G',xtype)
End
 
return .my.rxm~tan(x,xprec,xtype)
 
::routine rxmtanh public
Use Strict Arg x,xprec=(.my.rxm~precision)
 
If datatype(x,'NUM')=0 Then Do
-- Say 'Argument 1 must be a number'
Raise Syntax 88.902 array(1,x)
End
 
If datatype(xprec,'W')=0 Then Do
-- Say 'Argument 2 must be a positive whole number'
Raise Syntax 88.905 array(2,xprec)
End
 
If xprec<1 | 999999<xprec Then Do
-- Say 'Argument 2 must be a whole number between 1 and 999999'
Raise Syntax 88.907 array(2,1,999999,xprec)
End
 
return .my.rxm~tanh(x,xprec)
 
::routine rxmhelp public
Use Arg xprec=(.my.rxm~precision),xtype=(.my.rxm~type)
Say 'precision='xprec
Say ' type='xtype
Parse source s; Say ' source='s
Parse version v; Say ' version='v
Do si=2 To 5
Say substr(sourceline(si),3)
End
Say 'You can change the default precision and type as follows:'
Say " .locaL~my.rxm~precision=50"
Say " .locaL~my.rxm~type='R'"
return 0

Oz[edit]

declare
PI = 3.14159265
 
fun {FromDegrees Deg}
Deg * PI / 180.
end
 
fun {ToDegrees Rad}
Rad * 180. / PI
end
 
Radians = PI / 4.
Degrees = 45.
in
for F in [Sin Cos Tan] do
{System.showInfo {F Radians}#" "#{F {FromDegrees Degrees}}}
end
 
for I#F in [Asin#Sin Acos#Cos Atan#Tan] do
{System.showInfo {I {F Radians}}#" "#{ToDegrees {I {F Radians}}}}
end

PARI/GP[edit]

Pari accepts only radians; the conversion is simple but not included here.

cos(Pi/2)
sin(Pi/2)
tan(Pi/2)
acos(1)
asin(1)
atan(1)
Works with: PARI/GP version 2.4.3 and above
apply(f->f(1), [cos,sin,tan,acos,asin,atan])

Pascal[edit]

Library: math
Program TrigonometricFuntions(output);
 
uses
math;
 
var
radians, degree: double;
 
begin
radians := pi / 4.0;
degree := 45;
// Pascal works in radians. Necessary degree-radian conversions are shown.
writeln (sin(radians),' ', sin(degree/180*pi));
writeln (cos(radians),' ', cos(degree/180*pi));
writeln (tan(radians),' ', tan(degree/180*pi));
writeln ();
writeln (arcsin(sin(radians)),' Rad., or ', arcsin(sin(degree/180*pi))/pi*180,' Deg.');
writeln (arccos(cos(radians)),' Rad., or ', arccos(cos(degree/180*pi))/pi*180,' Deg.');
writeln (arctan(tan(radians)),' Rad., or ', arctan(tan(degree/180*pi))/pi*180,' Deg.');
// ( radians ) / pi * 180 = deg.
end.
Output:
 7.0710678118654750E-0001    7.0710678118654752E-0001
 7.0710678118654755E-0001    7.0710678118654752E-0001
 9.9999999999999994E-0001    1.0000000000000000E+0000

 7.8539816339744828E-0001  Rad., or  4.5000000000000000E+0001  Deg.
 7.8539816339744828E-0001  Rad., or  4.5000000000000000E+0001  Deg.
 7.8539816339744828E-0001  Rad., or  4.5000000000000000E+0001  Deg.

Perl[edit]

Works with: Perl version 5.8.8
use Math::Trig;
 
my $angle_degrees = 45;
my $angle_radians = pi / 4;
 
print sin($angle_radians), ' ', sin(deg2rad($angle_degrees)), "\n";
print cos($angle_radians), ' ', cos(deg2rad($angle_degrees)), "\n";
print tan($angle_radians), ' ', tan(deg2rad($angle_degrees)), "\n";
print cot($angle_radians), ' ', cot(deg2rad($angle_degrees)), "\n";
my $asin = asin(sin($angle_radians));
print $asin, ' ', rad2deg($asin), "\n";
my $acos = acos(cos($angle_radians));
print $acos, ' ', rad2deg($acos), "\n";
my $atan = atan(tan($angle_radians));
print $atan, ' ', rad2deg($atan), "\n";
my $acot = acot(cot($angle_radians));
print $acot, ' ', rad2deg($acot), "\n";
Output:
0.707106781186547 0.707106781186547
0.707106781186548 0.707106781186548
1 1
1 1
0.785398163397448 45
0.785398163397448 45
0.785398163397448 45
0.785398163397448 45

Perl 6[edit]

Works with: Rakudo version 2016.01
say sin(pi/3);
say cos(pi/4);
say tan(pi/6);
 
say asin(sqrt(3)/2);
say acos(1/sqrt 2);
say atan(1/sqrt 3);

Phix[edit]

?sin(PI/2)
?sin(90*PI/180)
?cos(0)
?cos(0*PI/180)
?tan(PI/4)
?tan(45*PI/180)
?arcsin(1)*2
?arcsin(1)*180/PI
?arccos(0)*2
?arccos(0)*180/PI
?arctan(1)*4
?arctan(1)*180/PI
Output:
1
1
1
1
1.0
1.0
3.141592654
90
3.141592654
90
3.141592654
45

PHP[edit]

$radians = M_PI / 4;
$degrees = 45 * M_PI / 180;
echo sin($radians) . " " . sin($degrees);
echo cos($radians) . " " . cos($degrees);
echo tan($radians) . " " . tan($degrees);
echo asin(sin($radians)) . " " . asin(sin($radians)) * 180 / M_PI;
echo acos(cos($radians)) . " " . acos(cos($radians)) * 180 / M_PI;
echo atan(tan($radians)) . " " . atan(tan($radians)) * 180 / M_PI;

PicoLisp[edit]

(load "@lib/math.l")
 
(de dtor (Deg)
(*/ Deg pi 180.0) )
 
(de rtod (Rad)
(*/ Rad 180.0 pi) )
 
(prinl
(format (sin (/ pi 4)) *Scl) " " (format (sin (dtor 45.0)) *Scl) )
(prinl
(format (cos (/ pi 4)) *Scl) " " (format (cos (dtor 45.0)) *Scl) )
(prinl
(format (tan (/ pi 4)) *Scl) " " (format (tan (dtor 45.0)) *Scl) )
(prinl
(format (asin (sin (/ pi 4))) *Scl) " " (format (rtod (asin (sin (dtor 45.0)))) *Scl) )
(prinl
(format (acos (cos (/ pi 4))) *Scl) " " (format (rtod (acos (cos (dtor 45.0)))) *Scl) )
(prinl
(format (atan (tan (/ pi 4))) *Scl) " " (format (rtod (atan (tan (dtor 45.0)))) *Scl) )
Output:
0.707107 0.707107
0.707107 0.707107
1.000000 1.000000
0.785398 44.999986
0.785398 44.999986
0.785398 44.999986

PL/I[edit]

 
declare (x, xd, y, v) float;
 
x = 0.5; xd = 45;
 
/* angle in radians: */
v = sin(x); y = asin(v); put skip list (y);
v = cos(x); y = acos(v); put skip list (y);
v = tan(x); y = atan(v); put skip list (y);
 
/* angle in degrees: */
v = sind(xd); put skip list (v);
v = cosd(xd); put skip list (v);
v = tand(xd); y = atand(v); put skip list (y);
 
/* hyperbolic functions: */
v = sinh(x); put skip list (v);
v = cosh(x); put skip list (v);
v = tanh(x); y = atanh(v); put skip list (y);
 

Results:

 5.00000E-0001 
 5.00000E-0001 
 5.00000E-0001 
 7.07107E-0001 
 7.07107E-0001 
 4.50000E+0001 
 5.21095E-0001 
 1.12763E+0000 
 5.00000E-0001 

PL/SQL[edit]

The transcendental functions COS, COSH, EXP, LN, LOG, SIN, SINH, SQRT, TAN, and TANH are accurate to 36 decimal digits. The transcendental functions ACOS, ASIN, ATAN, and ATAN2 are accurate to 30 decimal digits.

DECLARE
pi NUMBER := 4 * ATAN(1);
radians NUMBER := pi / 4;
degrees NUMBER := 45.0;
BEGIN
DBMS_OUTPUT.put_line(SIN(radians) || ' ' || SIN(degrees * pi/180) );
DBMS_OUTPUT.put_line(COS(radians) || ' ' || COS(degrees * pi/180) );
DBMS_OUTPUT.put_line(TAN(radians) || ' ' || TAN(degrees * pi/180) );
DBMS_OUTPUT.put_line(ASIN(SIN(radians)) || ' ' || ASIN(SIN(degrees * pi/180)) * 180/pi);
DBMS_OUTPUT.put_line(ACOS(COS(radians)) || ' ' || ACOS(COS(degrees * pi/180)) * 180/pi);
DBMS_OUTPUT.put_line(ATAN(TAN(radians)) || ' ' || ATAN(TAN(degrees * pi/180)) * 180/pi);
END;
Output:
,7071067811865475244008443621048490392889 ,7071067811865475244008443621048490392893
,7071067811865475244008443621048490392783 ,7071067811865475244008443621048490392779
1,00000000000000000000000000000000000001 1,00000000000000000000000000000000000002
,7853981633974483096156608458198656891236 44,99999999999999999999999999999942521259
,7853981633974483096156608458198857529988 45,00000000000000000000000000000057478811
,7853981633974483096156608458198757210578 45,00000000000000000000000000000000000067

The following trigonometric functions are also available

ATAN2(n1,n2) --Arctangent(y/x), -pi < result <= +pi
SINH(n) --Hyperbolic sine
COSH(n) --Hyperbolic cosine
TANH(n) --Hyperbolic tangent

Pop11[edit]

Pop11 trigonometric functions accept both degrees and radians. In default mode argument is in degrees, after setting 'popradians' flag to 'true' arguments are in radians.

sin(30) =>
cos(45) =>
tan(45) =>
arcsin(0.7) =>
arccos(0.7) =>
arctan(0.7) =>
;;; switch to radians
true -> popradians;
 
sin(pi*30/180) =>
cos(pi*45/180) =>
tan(pi*45/180) =>
arcsin(0.7) =>
arccos(0.7) =>
arctan(0.7) =>

PostScript[edit]

 
90 sin =
 
60 cos =
 
%tan of 45 degrees
 
45 sin 45 cos div =
 
%inverse tan ( arc tan of sqrt 3)
 
3 sqrt 1 atan =
 
Output:
1.0

0.5

1.0

60.0

PowerShell[edit]

Translation of: C
$rad = [Math]::PI / 4
$deg = 45
'{0,10} {1,10}' -f 'Radians','Degrees'
'{0,10:N6} {1,10:N6}' -f [Math]::Sin($rad), [Math]::Sin($deg * [Math]::PI / 180)
'{0,10:N6} {1,10:N6}' -f [Math]::Cos($rad), [Math]::Cos($deg * [Math]::PI / 180)
'{0,10:N6} {1,10:N6}' -f [Math]::Tan($rad), [Math]::Tan($deg * [Math]::PI / 180)
$temp = [Math]::Asin([Math]::Sin($rad))
'{0,10:N6} {1,10:N6}' -f $temp, ($temp * 180 / [Math]::PI)
$temp = [Math]::Acos([Math]::Cos($rad))
'{0,10:N6} {1,10:N6}' -f $temp, ($temp * 180 / [Math]::PI)
$temp = [Math]::Atan([Math]::Tan($rad))
'{0,10:N6} {1,10:N6}' -f $temp, ($temp * 180 / [Math]::PI)
Output:
   Radians    Degrees
  0,707107   0,707107
  0,707107   0,707107
  1,000000   1,000000
  0,785398  45,000000
  0,785398  45,000000
  0,785398  45,000000

A More "PowerShelly" Way[edit]

I would send the output as an array of objects containing the ([double]) properties: Radians and Degrees. Notice the difference between the last decimal place in the first two objects. If you were calculating coordinates as a civil engineer or land surveyor this difference could affect your measurments. Additionally, the output is an array of objects containing [double] values rather than an array of strings.

 
$radians = [Math]::PI / 4
$degrees = 45
 
[PSCustomObject]@{Radians=[Math]::Sin($radians); Degrees=[Math]::Sin($degrees * [Math]::PI / 180)}
[PSCustomObject]@{Radians=[Math]::Cos($radians); Degrees=[Math]::Cos($degrees * [Math]::PI / 180)}
[PSCustomObject]@{Radians=[Math]::Tan($radians); Degrees=[Math]::Tan($degrees * [Math]::PI / 180)}
 
[double]$tempVar = [Math]::Asin([Math]::Sin($radians))
[PSCustomObject]@{Radians=$tempVar; Degrees=$tempVar * 180 / [Math]::PI}
 
[double]$tempVar = [Math]::Acos([Math]::Cos($radians))
[PSCustomObject]@{Radians=$tempVar; Degrees=$tempVar * 180 / [Math]::PI}
 
[double]$tempVar = [Math]::Atan([Math]::Tan($radians))
[PSCustomObject]@{Radians=$tempVar; Degrees=$tempVar * 180 / [Math]::PI}
 
Output:
          Radians           Degrees
          -------           -------
0.707106781186547 0.707106781186547
0.707106781186548 0.707106781186548
                1                 1
0.785398163397448                45
0.785398163397448                45
0.785398163397448                45

PureBasic[edit]

OpenConsole()
 
Macro DegToRad(deg)
deg*#PI/180
EndMacro
Macro RadToDeg(rad)
rad*180/#PI
EndMacro
 
degree = 45
radians.f = #PI/4
 
PrintN(StrF(Sin(DegToRad(degree)))+" "+StrF(Sin(radians)))
PrintN(StrF(Cos(DegToRad(degree)))+" "+StrF(Cos(radians)))
PrintN(StrF(Tan(DegToRad(degree)))+" "+StrF(Tan(radians)))
 
arcsin.f = ASin(Sin(radians))
PrintN(StrF(arcsin)+" "+Str(RadToDeg(arcsin)))
arccos.f = ACos(Cos(radians))
PrintN(StrF(arccos)+" "+Str(RadToDeg(arccos)))
arctan.f = ATan(Tan(radians))
PrintN(StrF(arctan)+" "+Str(RadToDeg(arctan)))
 
Input()
Output:
0.707107 0.707107
0.707107 0.707107
1.000000 1.000000
0.785398 45
0.785398 45
0.785398 45

Python[edit]

Python's math module contains all six functions.
The functions all accept radians only, so conversion is necessary when dealing with degrees.
The math module also has degrees() and radians() functions for easy conversion.

Python 3.2.2 (default, Sep  4 2011, 09:51:08) [MSC v.1500 32 bit (Intel)] on win32
Type "copyright", "credits" or "license()" for more information.
>>> from math import degrees, radians, sin, cos, tan, asin, acos, atan, pi
>>> rad, deg = pi/4, 45.0
>>> print("Sine:", sin(rad), sin(radians(deg)))
Sine: 0.7071067811865475 0.7071067811865475
>>> print("Cosine:", cos(rad), cos(radians(deg)))
Cosine: 0.7071067811865476 0.7071067811865476
>>> print("Tangent:", tan(rad), tan(radians(deg)))
Tangent: 0.9999999999999999 0.9999999999999999
>>> arcsine = asin(sin(rad))
>>> print("Arcsine:", arcsine, degrees(arcsine))
Arcsine: 0.7853981633974482 44.99999999999999
>>> arccosine = acos(cos(rad))
>>> print("Arccosine:", arccosine, degrees(arccosine))
Arccosine: 0.7853981633974483 45.0
>>> arctangent = atan(tan(rad))
>>> print("Arctangent:", arctangent, degrees(arctangent))
Arctangent: 0.7853981633974483 45.0
>>>

R[edit]

deg <- function(radians) 180*radians/pi
rad <- function(degrees) degrees*pi/180
sind <- function(ang) sin(rad(ang))
cosd <- function(ang) cos(rad(ang))
tand <- function(ang) tan(rad(ang))
asind <- function(v) deg(asin(v))
acosd <- function(v) deg(acos(v))
atand <- function(v) deg(atan(v))
 
r <- pi/3
rd <- deg(r)
 
print( c( sin(r), sind(rd)) )
print( c( cos(r), cosd(rd)) )
print( c( tan(r), tand(rd)) )
 
S <- sin(pi/4)
C <- cos(pi/3)
T <- tan(pi/4)
 
print( c( asin(S), asind(S) ) )
print( c( acos(C), acosd(C) ) )
print( c( atan(T), atand(T) ) )

Racket[edit]

#lang racket
(define radians (/ pi 4))
(define degrees 45)
 
(displayln (format "~a ~a" (sin radians) (sin (* degrees (/ pi 180)))))
 
(displayln (format "~a ~a" (cos radians) (cos (* degrees (/ pi 180)))))
 
(displayln (format "~a ~a" (tan radians) (tan (* degrees (/ pi 180)))))
 
(define arcsin (asin (sin radians)))
(displayln (format "~a ~a" arcsin (* arcsin (/ 180 pi))))
 
(define arccos (acos (cos radians)))
(displayln (format "~a ~a" arccos (* arccos (/ 180 pi))))
 
(define arctan (atan (tan radians)))
(display (format "~a ~a" arctan (* arctan (/ 180 pi))))

RapidQ[edit]

$APPTYPE CONSOLE
$TYPECHECK ON
 
SUB pause(prompt$)
PRINT prompt$
DO
SLEEP .1
LOOP UNTIL LEN(INKEY$) > 0
END SUB
 
'MAIN
DEFDBL pi , radians , degrees , deg2rad
pi = 4 * ATAN(1)
deg2rad = pi / 180
radians = pi / 4
degrees = 45 * deg2rad
 
PRINT format$("%.6n" , SIN(radians)) + " " + format$("%.6n" , SIN(degrees))
PRINT format$("%.6n" , COS(radians)) + " " + format$("%.6n" , COS(degrees))
PRINT format$("%.6n" , TAN(radians)) + " " + format$("%.6n" , TAN(degrees))
 
DEFDBL temp = SIN(radians)
PRINT format$("%.6n" , ASIN(temp)) + " " + format$("%.6n" , ASIN(temp) / deg2rad)
 
temp = COS(radians)
PRINT format$("%.6n" , ACOS(temp)) + " " + format$("%.6n" , ACOS(temp) / deg2rad)
 
temp = TAN(radians)
PRINT format$("%.6n" , ATAN(temp)) + " " + format$("%.6n" , ATAN(temp) / deg2rad)
 
pause("Press any key to continue.")
 
END 'MAIN

REBOL[edit]

rebol [
Title: "Trigonometric Functions"
Author: oofoe
Date: 2009-12-07
URL: http://rosettacode.org/wiki/Trigonometric_Functions
]

 
radians: pi / 4 degrees: 45.0
 
; Unlike most languages, REBOL's trig functions work in degrees unless
; you specify differently.
 
print [sine/radians radians sine degrees]
print [cosine/radians radians cosine degrees]
print [tangent/radians radians tangent degrees]
 
d2r: func [
"Convert degrees to radians."
d [number!] "Degrees"
][d * pi / 180]
 
arcsin: arcsine sine degrees
print [d2r arcsin arcsin]
 
arccos: arccosine cosine degrees
print [d2r arccos arccos]
 
arctan: arctangent tangent degrees
print [d2r arctan arctan]
Output:
0.707106781186547 0.707106781186547
0.707106781186548 0.707106781186548
1.0 1.0
0.785398163397448 45.0
0.785398163397448 45.0
0.785398163397448 45.0

REXX[edit]

The REXX language doesn't have any trig functions (or for that matter, a square root [SQRT] function), so if higher math
functions are wanted, you have to roll your own. Some of the normal/regular trigonometric functions are included here.

 ┌──────────────────────────────────────────────────────────────────────────┐
│ One common method that ensures enough accuracy in REXX is specifying │
│ more precision (via NUMERIC DIGITS nnn) than is needed, and then
│ displaying the number of digits that are desired, or the number(s)
│ could be re-normalized using the FORMAT BIF.
│ │
│ The technique used (below) is to set the numeric digits ten higher │
│ than the desired digits, as specified by the SHOWDIGS variable.
└──────────────────────────────────────────────────────────────────────────┘

Most math (POW, EXP, LOG, LN, GAMMA, etc.), trigonometric, and hyperbolic functions need only five extra digits, but ten
extra digits is safer in case the argument is close to an asymptotic point or a multiple or fractional part of pi or somesuch.
It should also be noted that both the pi and e constants have only around 77 decimal digits as included here, if more
precision is needed, those constants should be extended.   Both pi and e could've been shown with more precision,
but having large precision numbers would add to this REXX program's length.   If anybody wishes to see this REXX version of
extended digits for pi or e, I could extend them to any almost any precision (as a REXX constant).   Normally, a REXX
(external) subroutine is used for such purposes so as to not make the program using the constant unwieldy large.

/*REXX program demonstrates some common trig functions (30 digits shown)*/
showdigs=30 /*show only 30 digits of number. */
numeric digits showdigs+10 /*DIGITS default is 9, but use */
/*extra digs to prevent rounding.*/
 
say 'Using' showdigs 'decimal digits precision.'; say
 
do j=-180 to +180 by 15 /*let's just do a half-Monty. */
stuff = right(j,4) 'degrees, rads='show( d2r(j)),
' sin='show(sinD(j)),
' cos='show(cosD(J))
/*don't let TAN go postal.*/
if abs(j)\==90 then stuff=stuff ' tan='show(tanD(j))
say stuff
end /*j*/
 
say; do k=-1 to +1 by 1/2 /*keep the Arc-functions happy. */
say right(k,4) 'radians, degs='show( r2d(k)),
' Acos='show(Acos(k)),
' Asin='show(Asin(k)),
' Atan='show(Atan(k))
end /*k*/
exit /*stick a fork in it, we're done.*/
/*──────────────────────────────────subroutines─────────────────────────*/
Asin: procedure; parse arg x 1 z 1 o 1 p; a=abs(x); aa=a*a
if a>1 then call AsinErr x /*X arg is out of range.*/
if a>=sqrt(2)*.5 then return sign(x)*acos(sqrt(1-aa), '-ASIN')
do j=2 by 2 until p=z; p=z; o=o*aa*(j-1)/j; z=z+o/(j+1); end
return z /* [↑] compute until no noise.*/
 
Atan: procedure; parse arg x; if abs(x)=1 then return pi() * .25 * sign(x)
return Asin(x/sqrt(1+x*x) )
 
cos: procedure; parse arg x; x=r2r(x); a=abs(x); hpi=pi*.5
numeric fuzz min(6,digits()-3); if a=pi() then return -1
if a=hpi | a=hpi*3 then return 0; if a=pi()/3 then return .5
if a=pi()*2/3 then return -.5; return .sinCos(1,-1)
 
sin: procedure; parse arg x; x=r2r(x); numeric fuzz $fuzz(5, 3)
if x=pi*.5 then return 1; if x==pi*1.5 then return -1
if abs(x)=pi | x=0 then return 0; return .sinCos(x,1)
 
.sinCos: parse arg z 1 _,i; q=x*x
do k=2 by 2 until p=z; p=z; _=-_*q/(k*(k+i)); z=z+_; end /*k*/
return z
 
sqrt: procedure; parse arg x; if x=0 then return 0; d=digits(); i=; m.=9
numeric digits 9; numeric form; h=d+6; if x<0 then do; x=-x; i='i'; end
parse value format(x,2,1,,0) 'E0' with g 'E' _ .; g=g*.5'e'_%2
do j=0 while h>9; m.j=h; h=h%2+1; end /*j*/
do k=j+5 to 0 by -1; numeric digits m.k; g=(g+x/g)*.5; end /*k*/
numeric digits d; return (g/1)i /*make complex if X < 0.*/
 
 
e: e=2.7182818284590452353602874713526624977572470936999595749669676277240766303535
return e /*Note: the actual E subroutine returns E's accuracy that */
/*matches the current NUMERIC DIGITS, up to 1 million digits.*/
 
exp: procedure; parse arg x; ix=x%1; if abs(x-ix)>.5 then ix=ix+sign(x); x=x-ix
z=1; _=1; w=z; do j=1; _=_*x/j; z=(z+_)/1; if z==w then leave; w=z; end
if z\==0 then z=e()**ix*z; return z
 
pi: pi=3.1415926535897932384626433832795028841971693993751058209749445923078164062862
return pi /*Note: the actual PI subroutine returns PI's accuracy that */
/*matches the current NUMERIC DIGITS, up to 1 million digits.*/
/*John Machin's formula is used for calculating more digits. */
 
$fuzz: return min(arg(1), max(1, digits() - arg(2) ) )
Acos: procedure; parse arg x; if x<-1|x>1 then call AcosErr; return pi()*.5-Asin(x)
AcosD: return r2d(Acos(arg(1)))
AsinD: return r2d(Asin(arg(1)))
cosD: return cos(d2r(arg(1)))
sinD: return sin(d2r(d2d(arg(1))))
tan: procedure; parse arg x; _=cos(x); if _=0 then call tanErr; return sin(x)/_
tanD: return tan(d2r(arg(1)))
d2d: return arg(1) // 360 /*normalize degrees ──► a unit circle*/
d2r: return r2r(d2d(arg(1))*pi() / 180) /*convert degrees ──► radians. */
r2d: return d2d((arg(1)*180 / pi())) /*convert radians ──► degrees. */
r2r: return arg(1) // (pi()*2) /*normalize radians ──► a unit circle*/
show: return left(left('',arg(1)>=0)format(arg(1),,showdigs)/1,showdigs)
tellErr: say; say '*** error! ***'; say; say arg(1); say; exit 13
tanErr: call tellErr 'tan(' || x") causes division by zero, X=" || x
AsinErr: call tellErr 'Asin(x), X must be in the range of -1 ──► +1, X=' || x
AcosErr: call tellErr 'Acos(x), X must be in the range of -1 ──► +1, X=' || x

Programming note:

 ╔═════════════════════════════════════════════════════════════════════════════╗
║ Functions that are not included here are (among others): ║
║ ║
║ some of the usual higher-math functions normally associated with trig ║
║ functions: POW, GAMMA, LGGAMMA, ERF, ERFC, ROOT, ATAN2, ║
║ LOG (LN), LOG2, LOG10, and all of the ║
║ hyperbolic trigonometric functions and their inverses (too many to list ║
║ here), ║
║ angle conversions/normalizations: degrees/radians/grads/mils: ║
║ a circle ≡ 2 pi radians ≡ 360 degrees ≡ 400 grads ≡ 6400 mils.
║ ║
║ Some of the other trigonometric functions are (hyphens added intentionally):║
║ ║
║ CHORD ║
║ COT (co-tangent)
║ CSC (co-secant)
║ CVC (co-versed cosine)
║ CVS (co-versed sine)
║ CXS (co-exsecant)
║ HAC (haver-cosine)
║ HAV (haver-sine ║
║ SEC (secant)
║ VCS (versed cosine or ver-cosine)
║ VSN (versed sine or ver-sine)
║ XCS (ex-secant)
║ COS/SIN/TAN cardinal (damped COS/SIN/TAN functions)
║ COS/SIN integral ║
║ ║
║ and all pertinent inverses of the above functions (AVSN, ACVS, ···).
╚═════════════════════════════════════════════════════════════════════════════╝

output

Using 30 decimal digits precision.

-180 degrees, rads=-3.141592653589793238462643383    sin= 0                                cos=-1                                tan= 0
-165 degrees, rads=-2.879793265790643801924089768    sin=-0.258819045102520762348898837    cos=-0.965925826289068286749743199    tan= 0.267949192431122706472553658
-150 degrees, rads=-2.617993877991494365385536152    sin=-0.5                              cos=-0.866025403784438646763723170    tan= 0.577350269189625764509148780
-135 degrees, rads=-2.356194490192344928846982537    sin=-0.707106781186547524400844362    cos=-0.707106781186547524400844362    tan= 1
-120 degrees, rads=-2.094395102393195492308428922    sin=-0.866025403784438646763723170    cos=-0.5                              tan= 1.732050807568877293527446341
-105 degrees, rads=-1.832595714594046055769875306    sin=-0.965925826289068286749743199    cos=-0.258819045102520762348898837    tan= 3.732050807568877293527446341
 -90 degrees, rads=-1.570796326794896619231321691    sin=-1                                cos= 0
 -75 degrees, rads=-1.308996938995747182692768076    sin=-0.965925826289068286749743199    cos= 0.258819045102520762348898837    tan=-3.732050807568877293527446341
 -60 degrees, rads=-1.047197551196597746154214461    sin=-0.866025403784438646763723170    cos= 0.5                              tan=-1.732050807568877293527446341
 -45 degrees, rads=-0.785398163397448309615660845    sin=-0.707106781186547524400844362    cos= 0.707106781186547524400844362    tan=-1
 -30 degrees, rads=-0.523598775598298873077107230    sin=-0.5                              cos= 0.866025403784438646763723170    tan=-0.577350269189625764509148780
 -15 degrees, rads=-0.261799387799149436538553615    sin=-0.258819045102520762348898837    cos= 0.965925826289068286749743199    tan=-0.267949192431122706472553658
   0 degrees, rads= 0                                sin= 0                                cos= 1                                tan= 0
  15 degrees, rads= 0.261799387799149436538553615    sin= 0.258819045102520762348898837    cos= 0.965925826289068286749743199    tan= 0.267949192431122706472553658
  30 degrees, rads= 0.523598775598298873077107230    sin= 0.5                              cos= 0.866025403784438646763723170    tan= 0.577350269189625764509148780
  45 degrees, rads= 0.785398163397448309615660845    sin= 0.707106781186547524400844362    cos= 0.707106781186547524400844362    tan= 1
  60 degrees, rads= 1.047197551196597746154214461    sin= 0.866025403784438646763723170    cos= 0.5                              tan= 1.732050807568877293527446341
  75 degrees, rads= 1.308996938995747182692768076    sin= 0.965925826289068286749743199    cos= 0.258819045102520762348898837    tan= 3.732050807568877293527446341
  90 degrees, rads= 1.570796326794896619231321691    sin= 1                                cos= 0
 105 degrees, rads= 1.832595714594046055769875306    sin= 0.965925826289068286749743199    cos=-0.258819045102520762348898837    tan=-3.732050807568877293527446341
 120 degrees, rads= 2.094395102393195492308428922    sin= 0.866025403784438646763723170    cos=-0.5                              tan=-1.732050807568877293527446341
 135 degrees, rads= 2.356194490192344928846982537    sin= 0.707106781186547524400844362    cos=-0.707106781186547524400844362    tan=-1
 150 degrees, rads= 2.617993877991494365385536152    sin= 0.5                              cos=-0.866025403784438646763723170    tan=-0.577350269189625764509148780
 165 degrees, rads= 2.879793265790643801924089768    sin= 0.258819045102520762348898837    cos=-0.965925826289068286749743199    tan=-0.267949192431122706472553658
 180 degrees, rads= 3.141592653589793238462643383    sin= 0                                cos=-1                                tan= 0

  -1 radians, degs=-57.29577951308232087679815481   Acos= 3.141592653589793238462643383   Asin=-1.570796326794896619231321691   Atan=-0.785398163397448309615660845
-0.5 radians, degs=-28.64788975654116043839907740   Acos= 2.094395102393195492308428922   Asin=-0.523598775598298873077107230   Atan=-0.463647609000806116214256231
   0 radians, degs= 0                               Acos= 1.570796326794896619231321691   Asin= 0                               Atan= 0
 0.5 radians, degs= 28.64788975654116043839907740   Acos= 1.047197551196597746154214461   Asin= 0.523598775598298873077107230   Atan= 0.463647609000806116214256231
 1.0 radians, degs= 57.29577951308232087679815481   Acos= 0                               Asin= 1.570796326794896619231321691   Atan= 0.785398163397448309615660845

Ring[edit]

 
pi = 3.14
decimals(8)
see "sin(pi/4.0) = " + sin(pi/4.0) + nl
see "cos(pi/4.0) = " + cos(pi/4.0) + nl
see "tan(pi/4.0) = " + tan(pi/4.0)+ nl
see "asin(sin(pi/4.0)) = " + asin(sin(pi/4.0)) + nl
see "acos(cos(pi/4.0)) = " + acos(cos(pi/4.0)) + nl
see "atan(tan(pi/4.0)) = " + atan(tan(pi/4.0)) + nl
see "atan2(3,4) = " + atan2(3,4) + nl
 

Ruby[edit]

Ruby's Math module contains all six functions. The functions all accept radians only, so conversion is necessary when dealing with degrees.

radians = Math::PI / 4
degrees = 45.0
 
def deg2rad(d)
d * Math::PI / 180
end
 
def rad2deg(r)
r * 180 / Math::PI
end
 
#sine
puts "#{Math.sin(radians)} #{Math.sin(deg2rad(degrees))}"
#cosine
puts "#{Math.cos(radians)} #{Math.cos(deg2rad(degrees))}"
#tangent
puts "#{Math.tan(radians)} #{Math.tan(deg2rad(degrees))}"
#arcsine
arcsin = Math.asin(Math.sin(radians))
puts "#{arcsin} #{rad2deg(arcsin)}"
#arccosine
arccos = Math.acos(Math.cos(radians))
puts "#{arccos} #{rad2deg(arccos)}"
#arctangent
arctan = Math.atan(Math.tan(radians))
puts "#{arctan} #{rad2deg(arctan)}"
Output:
0.7071067811865475 0.7071067811865475
0.7071067811865476 0.7071067811865476
0.9999999999999999 0.9999999999999999
0.7853981633974482 44.99999999999999
0.7853981633974483 45.0
0.7853981633974483 45.0

BigDecimal[edit]

If you want more digits in the answer, then you can use the BigDecimal class. BigMath only has big versions of sine, cosine, and arctangent; so we must implement tangent, arcsine and arccosine.

Translation of: bc
Works with: Ruby version 1.9
require 'bigdecimal'       # BigDecimal
require 'bigdecimal/math' # BigMath
 
include BigMath # Allow sin(x, prec) instead of BigMath.sin(x, prec).
 
# Tangent of _x_.
def tan(x, prec)
sin(x, prec) / cos(x, prec)
end
 
# Arcsine of _y_, domain [-1, 1], range [-pi/2, pi/2].
def asin(y, prec)
# Handle angles with no tangent.
return -PI / 2 if y == -1
return PI / 2 if y == 1
 
# Tangent of angle is y / x, where x^2 + y^2 = 1.
atan(y / sqrt(1 - y * y, prec), prec)
end
 
# Arccosine of _x_, domain [-1, 1], range [0, pi].
def acos(x, prec)
# Handle angle with no tangent.
return PI / 2 if x == 0
 
# Tangent of angle is y / x, where x^2 + y^2 = 1.
a = atan(sqrt(1 - x * x, prec) / x, prec)
if a < 0
a + PI(prec)
else
a
end
end
 
 
prec = 52
pi = PI(prec)
degrees = pi / 180 # one degree in radians
 
b1 = BigDecimal.new "1"
b2 = BigDecimal.new "2"
b3 = BigDecimal.new "3"
 
f = proc { |big| big.round(50).to_s('F') }
print("Using radians:",
"\n sin(-pi / 6) = ", f[ sin(-pi / 6, prec) ],
"\n cos(3 * pi / 4) = ", f[ cos(3 * pi / 4, prec) ],
"\n tan(pi / 3) = ", f[ tan(pi / 3, prec) ],
"\n asin(-1 / 2) = ", f[ asin(-b1 / 2, prec) ],
"\n acos(-sqrt(2) / 2) = ", f[ acos(-sqrt(b2, prec) / 2, prec) ],
"\n atan(sqrt(3)) = ", f[ atan(sqrt(b3, prec), prec) ],
"\n")
print("Using degrees:",
"\n sin(-30) = ", f[ sin(-30 * degrees, prec) ],
"\n cos(135) = ", f[ cos(135 * degrees, prec) ],
"\n tan(60) = ", f[ tan(60 * degrees, prec) ],
"\n asin(-1 / 2) = ",
f[ asin(-b1 / 2, prec) / degrees ],
"\n acos(-sqrt(2) / 2) = ",
f[ acos(-sqrt(b2, prec) / 2, prec) / degrees ],
"\n atan(sqrt(3)) = ",
f[ atan(sqrt(b3, prec), prec) / degrees ],
"\n")
Output:
Using radians:
  sin(-pi / 6) = -0.5
  cos(3 * pi / 4) = -0.70710678118654752440084436210484903928483593768847
  tan(pi / 3) = 1.73205080756887729352744634150587236694280525381038
  asin(-1 / 2) = -0.52359877559829887307710723054658381403286156656252
  acos(-sqrt(2) / 2) = 2.35619449019234492884698253745962716314787704953133
  atan(sqrt(3)) = 1.04719755119659774615421446109316762806572313312504
Using degrees:
  sin(-30) = -0.5
  cos(135) = -0.70710678118654752440084436210484903928483593768847
  tan(60) = 1.73205080756887729352744634150587236694280525381038
  asin(-1 / 2) = -30.0
  acos(-sqrt(2) / 2) = 135.0
  atan(sqrt(3)) = 60.0

Run BASIC[edit]

' Find these three ratios:  Sine, Cosine, Tangent.  (These ratios have NO units.)
 
deg = 45.0
' Run BASIC works in radians; so, first convert deg to rad as shown in next line.
rad = deg * (atn(1)/45)
print "Ratios for a "; deg; " degree angle, (or "; rad; " radian angle.)"
print "Sine: "; SIN(rad)
print "Cosine: "; COS(rad)
print "Tangent: "; TAN(rad)
 
print "Inverse Functions - - (Using above ratios)"
' Now, use those ratios to work backwards to show their original angle in radians.
' Also, use this: rad / (atn(1)/45) = deg (To change radians to degrees.)
print "Arcsine: "; ASN(SIN(rad)); " radians, (or "; ASN(SIN(rad))/(atn(1)/45); " degrees)"
print "Arccosine: "; ACS(COS(rad)); " radians, (or "; ACS(COS(rad))/(atn(1)/45); " degrees)"
print "Arctangent: "; ATN(TAN(rad)); " radians, (or "; ATN(TAN(rad))/(atn(1)/45); " degrees)"
 
' This code also works in Liberty BASIC.
' The above (atn(1)/45) = approx .01745329252
Output:
Ratios for a 45.0 degree angle, (or 0.785398163 radian angle.)
Sine:        0.707106781
Cosine:      0.707106781
Tangent:     1.0
Inverse Functions - - (Using above ratios)
Arcsine:     0.785398163 radians, (or 45.0 degrees)
Arccosine:   0.785398163 radians, (or 45.0 degrees)
Arctangent:  0.785398163 radians, (or 45.0 degrees)

SAS[edit]

data _null_;
pi = 4*atan(1);
deg = 30;
rad = pi/6;
k = pi/180;
x = 0.2;
 
a = sin(rad);
b = sin(deg*k);
put a b;
 
a = cos(rad);
b = cos(deg*k);
put a b;
 
a = tan(rad);
b = tan(deg*k);
put a b;
 
a=arsin(x);
b=arsin(x)/k;
put a b;
 
a=arcos(x);
b=arcos(x)/k;
put a b;
 
a=atan(x);
b=atan(x)/k;
put a b;
run;

Scala[edit]

Library: Scala
import scala.math._
 
object Gonio extends App {
//Pi / 4 rad is 45 degrees. All answers should be the same.
val radians = Pi / 4
val degrees = 45.0
 
println(s"${sin(radians)} ${sin(toRadians(degrees))}")
//cosine
println(s"${cos(radians)} ${cos(toRadians(degrees))}")
//tangent
println(s"${tan(radians)} ${tan(toRadians(degrees))}")
//arcsine
val bgsin = asin(sin(radians))
println(s"$bgsin ${toDegrees(bgsin)}")
val bgcos = acos(cos(radians))
println(s"$bgcos ${toDegrees(bgcos)}")
//arctangent
val bgtan = atan(tan(radians))
println(s"$bgtan ${toDegrees(bgtan)}")
val bgtan2 = atan2(1, 1)
println(s"$bgtan ${toDegrees(bgtan)}")
}

Scheme[edit]

(define pi (* 4 (atan 1)))
 
(define radians (/ pi 4))
(define degrees 45)
 
(display (sin radians))
(display " ")
(display (sin (* degrees (/ pi 180))))
(newline)
 
(display (cos radians))
(display " ")
(display (cos (* degrees (/ pi 180))))
(newline)
 
(display (tan radians))
(display " ")
(display (tan (* degrees (/ pi 180))))
(newline)
 
(define arcsin (asin (sin radians)))
(display arcsin)
(display " ")
(display (* arcsin (/ 180 pi)))
(newline)
 
(define arccos (acos (cos radians)))
(display arccos)
(display " ")
(display (* arccos (/ 180 pi)))
(newline)
 
(define arctan (atan (tan radians)))
(display arctan)
(display " ")
(display (* arctan (/ 180 pi)))
(newline)

Seed7[edit]

The example below uses the libaray math.s7i, which defines, besides many other functions, sin, cos, tan, asin, acos and atan.

$ include "seed7_05.s7i";
include "float.s7i";
include "math.s7i";
 
const proc: main is func
local
const float: radians is PI / 4.0;
const float: degrees is 45.0;
begin
writeln(" radians degrees");
writeln("sine: " <& sin(radians) digits 5 <& sin(degrees * PI / 180.0) digits 5 lpad 9);
writeln("cosine: " <& cos(radians) digits 5 <& cos(degrees * PI / 180.0) digits 5 lpad 9);
writeln("tangent: " <& tan(radians) digits 5 <& tan(degrees * PI / 180.0) digits 5 lpad 9);
writeln("arcsine: " <& asin(0.70710677) digits 5 <& asin(0.70710677) * 180.0 / PI digits 5 lpad 9);
writeln("arccosine: " <& acos(0.70710677) digits 5 <& acos(0.70710677) * 180.0 / PI digits 5 lpad 9);
writeln("arctangent: " <& atan(1.0) digits 5 <& atan(1.0) * 180.0 / PI digits 5 lpad 9);
end func;
Output:
            radians  degrees
sine:       0.70711  0.70711
cosine:     0.70711  0.70711
tangent:    1.00000  1.00000
arcsine:    0.78540 45.00000
arccosine:  0.78540 45.00000
arctangent: 0.78540 45.00000

Sidef[edit]

var angle_deg = 45;
var angle_rad = Num.pi/4;
 
for arr in [
[sin(angle_rad), sin(deg2rad(angle_deg))],
[cos(angle_rad), cos(deg2rad(angle_deg))],
[tan(angle_rad), tan(deg2rad(angle_deg))],
[cot(angle_rad), cot(deg2rad(angle_deg))],
] {
say arr.join(" ");
}
 
for n in [
asin(sin(angle_rad)),
acos(cos(angle_rad)),
atan(tan(angle_rad)),
acot(cot(angle_rad)),
] {
say [n, rad2deg(n)].join(' ');
}
Output:
0.707106781186547 0.707106781186547
0.707106781186548 0.707106781186548
1 1
1 1
0.785398163397448 45
0.785398163397448 45
0.785398163397448 45
0.785398163397448 45

Stata[edit]

Stata computes only in radians, but the conversion is easy.

scalar deg=_pi/180
 
display cos(30*deg)
display sin(30*deg)
display tan(30*deg)
 
display cos(_pi/6)
display sin(_pi/6)
display tan(_pi/6)
 
display acos(0.5)
display asin(0.5)
display atan(0.5)

Tcl[edit]

The built-in functions only take radian arguments.

package require Tcl 8.5
 
proc PI {} {expr {4*atan(1)}}
proc deg2rad d {expr {$d/180*[PI]}}
proc rad2deg r {expr {$r*180/[PI]}}
 
namespace path ::tcl::mathfunc
 
proc trig degrees {
set radians [deg2rad $degrees]
puts [sin $radians]
puts [cos $radians]
puts [tan $radians]
set arcsin [asin [sin $radians]]; puts "$arcsin [rad2deg $arcsin]"
set arccos [acos [cos $radians]]; puts "$arccos [rad2deg $arccos]"
set arctan [atan [tan $radians]]; puts "$arctan [rad2deg $arctan]"
}
trig 60.0
0.8660254037844386
0.5000000000000001
1.7320508075688767
1.0471975511965976 59.99999999999999
1.0471975511965976 59.99999999999999
1.0471975511965976 59.99999999999999

XPL0[edit]

include c:\cxpl\codes;  \intrinsic 'code' declarations
def Pi = 3.14159265358979323846;
 
func real ATan(Y); \Arc tangent
real Y;
return ATan2(Y, 1.0);
 
func real Deg(X); \Convert radians to degrees
real X;
return 57.2957795130823 * X;
 
func real Rad(X); \Convert degrees to radians
real X;
return X / 57.2957795130823;
 
real A, B, C;
[A:= Sin(Pi/6.0);
RlOut(0, A); ChOut(0, 9\tab\); RlOut(0, Sin(Rad(30.0))); CrLf(0);
B:= Cos(Pi/6.0);
RlOut(0, B); ChOut(0, 9\tab\); RlOut(0, Cos(Rad(30.0))); CrLf(0);
C:= Tan(Pi/4.0);
RlOut(0, C); ChOut(0, 9\tab\); RlOut(0, Tan(Rad(45.0))); CrLf(0);
 
RlOut(0, ASin(A)); ChOut(0, 9\tab\); RlOut(0, Deg(ASin(A))); CrLf(0);
RlOut(0, ACos(B)); ChOut(0, 9\tab\); RlOut(0, Deg(ACos(B))); CrLf(0);
RlOut(0, ATan(C)); ChOut(0, 9\tab\); RlOut(0, Deg(ATan(C))); CrLf(0);
]
Output:
    0.50000         0.50000
    0.86603         0.86603
    1.00000         1.00000
    0.52360        30.00000
    0.52360        30.00000
    0.78540        45.00000

zkl[edit]

 
(30.0).toRad().sin() //-->0.5
(60.0).toRad().cos() //-->0.5
(45.0).toRad().tan() //-->1
(0.523599).sin() //-->0.5
etc
 
(0.5).asin() //-->0.523599
(0.5).acos() //-->1.0472
(1.0).atan() //-->0.785398
(1.0).atan().toDeg() //-->45
etc