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2013-04-11 01:07:29 -07:00 · 2013-04-11 01:07:29 -07:00 · 68f8f3e56b
commit 68f8f3e56b
parent b83f433714
14735 changed files with 178959 additions and 0 deletions
--- a/Task/Trigonometric-functions/0DESCRIPTION
+++ b/Task/Trigonometric-functions/0DESCRIPTION
@ -0,0 +1,2 @@
+{{omit from|GAP}}
+If your language has a library or built-in functions for trigonometry, show examples of sine, cosine, tangent, and their inverses 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 [[wp:List of trigonometric identities|known approximation or identity]].
--- a/Task/Trigonometric-functions/1META.yaml
+++ b/Task/Trigonometric-functions/1META.yaml
@ -0,0 +1,2 @@
+---
+note: Arithmetic operations
--- a/Task/Trigonometric-functions/ACL2/trigonometric-functions.acl2
+++ b/Task/Trigonometric-functions/ACL2/trigonometric-functions.acl2
@ -0,0 +1,79 @@
+(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 "~%")))
--- a/Task/Trigonometric-functions/ALGOL-68/trigonometric-functions.alg
+++ b/Task/Trigonometric-functions/ALGOL-68/trigonometric-functions.alg
@ -0,0 +1,22 @@
+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))
+)
--- a/Task/Trigonometric-functions/AWK/trigonometric-functions.awk
+++ b/Task/Trigonometric-functions/AWK/trigonometric-functions.awk
@ -0,0 +1,40 @@
+# 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
+}
--- a/Task/Trigonometric-functions/ActionScript/trigonometric-functions.as
+++ b/Task/Trigonometric-functions/ActionScript/trigonometric-functions.as
@ -0,0 +1,16 @@
+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);
--- a/Task/Trigonometric-functions/Ada/trigonometric-functions.ada
+++ b/Task/Trigonometric-functions/Ada/trigonometric-functions.ada
@ -0,0 +1,35 @@
+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;
--- a/Task/Trigonometric-functions/AutoHotkey/trigonometric-functions.ahk
+++ b/Task/Trigonometric-functions/AutoHotkey/trigonometric-functions.ahk
@ -0,0 +1,28 @@
+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
+*/
--- a/Task/Trigonometric-functions/BASIC/trigonometric-functions.basic
+++ b/Task/Trigonometric-functions/BASIC/trigonometric-functions.basic
@ -0,0 +1,15 @@
+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
--- a/Task/Trigonometric-functions/BBC-BASIC/trigonometric-functions.bbc
+++ b/Task/Trigonometric-functions/BBC-BASIC/trigonometric-functions.bbc
@ -0,0 +1,14 @@
+      @% = &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))
--- a/Task/Trigonometric-functions/C++/trigonometric-functions.cpp
+++ b/Task/Trigonometric-functions/C++/trigonometric-functions.cpp
@ -0,0 +1,31 @@
+#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;
+}
--- a/Task/Trigonometric-functions/C/trigonometric-functions.c
+++ b/Task/Trigonometric-functions/C/trigonometric-functions.c
@ -0,0 +1,27 @@
+#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;
+}
--- a/Task/Trigonometric-functions/Clojure/trigonometric-functions.clj
+++ b/Task/Trigonometric-functions/Clojure/trigonometric-functions.clj
@ -0,0 +1,16 @@
+(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)))
--- a/Task/Trigonometric-functions/Common-Lisp/trigonometric-functions.lisp
+++ b/Task/Trigonometric-functions/Common-Lisp/trigonometric-functions.lisp
@ -0,0 +1,16 @@
+(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))))
--- a/Task/Trigonometric-functions/D/trigonometric-functions.d
+++ b/Task/Trigonometric-functions/D/trigonometric-functions.d
@ -0,0 +1,21 @@
+import std.stdio, std.math;
+
+void main() {
+    enum real degrees = 45.0;
+    enum real t0 = degrees * PI / 180.0;
+    writeln("Reference:  0.7071067811865475244008");
+    writefln("Sine:       %.20f  %.20f", sin(PI_4), sin(t0));
+    writefln("Cosine:     %.20f  %.20f", cos(PI_4), cos(t0));
+    writefln("Tangent:    %.20f  %.20f", tan(PI_4), tan(t0));
+
+    writeln();
+    writeln("Reference:  0.7853981633974483096156");
+    immutable real t1 = asin(sin(PI_4));
+    writefln("Arcsine:    %.20f %.20f", t1, t1 * 180.0 / PI);
+
+    immutable real t2 = acos(cos(PI_4));
+    writefln("Arccosine:  %.20f %.20f", t2, t2 * 180.0 / PI);
+
+    immutable real t3 = atan(tan(PI_4));
+    writefln("Arctangent: %.20f %.20f", t3, t3 * 180.0 / PI);
+}
--- a/Task/Trigonometric-functions/E/trigonometric-functions.e
+++ b/Task/Trigonometric-functions/E/trigonometric-functions.e
@ -0,0 +1,16 @@
+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)}
+`)
--- a/Task/Trigonometric-functions/Erlang/trigonometric-functions-1.erl
+++ b/Task/Trigonometric-functions/Erlang/trigonometric-functions-1.erl
@ -0,0 +1,4 @@
+Deg=45.
+Rad=math:pi()/4.
+
+math:sin(Deg * math:pi() / 180)==math:sin(Rad).
--- a/Task/Trigonometric-functions/Erlang/trigonometric-functions-2.erl
+++ b/Task/Trigonometric-functions/Erlang/trigonometric-functions-2.erl
@ -0,0 +1 @@
+math:cos(Deg * math:pi() / 180)==math:cos(Rad).
--- a/Task/Trigonometric-functions/Erlang/trigonometric-functions-3.erl
+++ b/Task/Trigonometric-functions/Erlang/trigonometric-functions-3.erl
@ -0,0 +1 @@
+math:tan(Deg * math:pi() / 180)==math:tan(Rad).
--- a/Task/Trigonometric-functions/Erlang/trigonometric-functions-4.erl
+++ b/Task/Trigonometric-functions/Erlang/trigonometric-functions-4.erl
@ -0,0 +1,2 @@
+Temp = math:acos(math:cos(Rad)).
+Temp * 180 / math:pi()==Deg.
--- a/Task/Trigonometric-functions/Erlang/trigonometric-functions-5.erl
+++ b/Task/Trigonometric-functions/Erlang/trigonometric-functions-5.erl
@ -0,0 +1,2 @@
+Temp = math:atan(math:tan(Rad)).
+Temp * 180 / math:pi()==Deg.
--- a/Task/Trigonometric-functions/Fantom/trigonometric-functions.fantom
+++ b/Task/Trigonometric-functions/Fantom/trigonometric-functions.fantom
@ -0,0 +1,20 @@
+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)
+  }
+}
--- a/Task/Trigonometric-functions/Forth/trigonometric-functions.fth
+++ b/Task/Trigonometric-functions/Forth/trigonometric-functions.fth
@ -0,0 +1,8 @@
+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] )
--- a/Task/Trigonometric-functions/Fortran/trigonometric-functions-1.f
+++ b/Task/Trigonometric-functions/Fortran/trigonometric-functions-1.f
@ -0,0 +1,18 @@
+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
--- a/Task/Trigonometric-functions/Fortran/trigonometric-functions-2.f
+++ b/Task/Trigonometric-functions/Fortran/trigonometric-functions-2.f
@ -0,0 +1,4 @@
+ATAN2(y,x) ! Arctangent(y/x), ''-pi < result <= +pi''
+SINH(x)    ! Hyperbolic sine
+COSH(x)    ! Hyperbolic cosine
+TANH(x)    ! Hyperbolic tangent
--- a/Task/Trigonometric-functions/Go/trigonometric-functions.go
+++ b/Task/Trigonometric-functions/Go/trigonometric-functions.go
@ -0,0 +1,28 @@
+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))
+}
--- a/Task/Trigonometric-functions/Groovy/trigonometric-functions.groovy
+++ b/Task/Trigonometric-functions/Groovy/trigonometric-functions.groovy
@ -0,0 +1,12 @@
+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"
--- a/Task/Trigonometric-functions/Haskell/trigonometric-functions.hs
+++ b/Task/Trigonometric-functions/Haskell/trigonometric-functions.hs
@ -0,0 +1,10 @@
+fromDegrees deg = deg * pi / 180
+toDegrees   rad = rad * 180 / pi
+
+example = [
+  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)]
--- a/Task/Trigonometric-functions/HicEst/trigonometric-functions-1.hicest
+++ b/Task/Trigonometric-functions/HicEst/trigonometric-functions-1.hicest
@ -0,0 +1,12 @@
+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
--- a/Task/Trigonometric-functions/HicEst/trigonometric-functions-2.hicest
+++ b/Task/Trigonometric-functions/HicEst/trigonometric-functions-2.hicest
@ -0,0 +1,6 @@
+0.7071067812 0.7071067812
+0.7071067812 0.7071067812
+1 1
+0.7853981634 45
+0.7853981634 45
+0.7853981634 45
--- a/Task/Trigonometric-functions/IDL/trigonometric-functions-1.idl
+++ b/Task/Trigonometric-functions/IDL/trigonometric-functions-1.idl
@ -0,0 +1,2 @@
+deg = 35         ; arbitrary number of degrees
+rad = !dtor*deg  ; system variables !dtor and !radeg convert between rad and deg
--- a/Task/Trigonometric-functions/IDL/trigonometric-functions-2.idl
+++ b/Task/Trigonometric-functions/IDL/trigonometric-functions-2.idl
@ -0,0 +1,9 @@
+; 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
--- a/Task/Trigonometric-functions/IDL/trigonometric-functions-3.idl
+++ b/Task/Trigonometric-functions/IDL/trigonometric-functions-3.idl
@ -0,0 +1,5 @@
+; the hyperbolic versions exist and behave as expected:
+print, sinh(rad)                       ; etc
+
+; outputs
+;   0.649572
--- a/Task/Trigonometric-functions/IDL/trigonometric-functions-4.idl
+++ b/Task/Trigonometric-functions/IDL/trigonometric-functions-4.idl
@ -0,0 +1,8 @@
+;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
--- a/Task/Trigonometric-functions/IDL/trigonometric-functions-5.idl
+++ b/Task/Trigonometric-functions/IDL/trigonometric-functions-5.idl
@ -0,0 +1,6 @@
+; the trig functions behave as expected for complex arguments:
+x = complex(1,2)
+print,sin(x)
+
+; outputs
+; (      3.16578,      1.95960)
--- a/Task/Trigonometric-functions/IDL/trigonometric-functions-6.idl
+++ b/Task/Trigonometric-functions/IDL/trigonometric-functions-6.idl
@ -0,0 +1,8 @@
+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
--- a/Task/Trigonometric-functions/J/trigonometric-functions-1.j
+++ b/Task/Trigonometric-functions/J/trigonometric-functions-1.j
@ -0,0 +1 @@
+    >,:(1&o. ; 2&o. ; 3&o.) (4%~o. 1), 180%~o. 45
--- a/Task/Trigonometric-functions/J/trigonometric-functions-2.j
+++ b/Task/Trigonometric-functions/J/trigonometric-functions-2.j
@ -0,0 +1 @@
+    >,:([ , 180p_1&*)&.> (_1&o. ; _2&o. ; _3&o.) 0.5
--- a/Task/Trigonometric-functions/Java/trigonometric-functions.java
+++ b/Task/Trigonometric-functions/Java/trigonometric-functions.java
@ -0,0 +1,22 @@
+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));
+        }
+}
--- a/Task/Trigonometric-functions/JavaScript/trigonometric-functions.js
+++ b/Task/Trigonometric-functions/JavaScript/trigonometric-functions.js
@ -0,0 +1,22 @@
+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));
--- a/Task/Trigonometric-functions/Liberty-BASIC/trigonometric-functions.liberty
+++ b/Task/Trigonometric-functions/Liberty-BASIC/trigonometric-functions.liberty
@ -0,0 +1,14 @@
+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"
--- a/Task/Trigonometric-functions/Logo/trigonometric-functions-1.logo
+++ b/Task/Trigonometric-functions/Logo/trigonometric-functions-1.logo
@ -0,0 +1,7 @@
+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
--- a/Task/Trigonometric-functions/Logo/trigonometric-functions-2.logo
+++ b/Task/Trigonometric-functions/Logo/trigonometric-functions-2.logo
@ -0,0 +1,6 @@
+print sin 45
+print cos 45
+print arctan 1
+print radsin pi / 4
+print radcos pi / 4
+print 4 * radarctan 1
--- a/Task/Trigonometric-functions/Lua/trigonometric-functions.lua
+++ b/Task/Trigonometric-functions/Lua/trigonometric-functions.lua
@ -0,0 +1 @@
+print(math.cos(1), math.sin(1), math.tan(1), math.atan(1), math.atan2(3, 4))
--- a/Task/Trigonometric-functions/MATLAB/trigonometric-functions-1.m
+++ b/Task/Trigonometric-functions/MATLAB/trigonometric-functions-1.m
@ -0,0 +1,13 @@
+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
--- a/Task/Trigonometric-functions/MATLAB/trigonometric-functions-2.m
+++ b/Task/Trigonometric-functions/MATLAB/trigonometric-functions-2.m
@ -0,0 +1,15 @@
+>> 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
--- a/Task/Trigonometric-functions/MAXScript/trigonometric-functions.maxscript
+++ b/Task/Trigonometric-functions/MAXScript/trigonometric-functions.maxscript
@ -0,0 +1,21 @@
+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))
--- a/Task/Trigonometric-functions/Mathematica/trigonometric-functions.math
+++ b/Task/Trigonometric-functions/Mathematica/trigonometric-functions.math
@ -0,0 +1,9 @@
+Sin[1]
+Cos[1]
+Tan[1]
+ArcSin[1]
+ArcCos[1]
+ArcTan[1]
+Sin[90 Degree]
+Cos[90 Degree]
+Tan[90 Degree]
--- a/Task/Trigonometric-functions/Maxima/trigonometric-functions.maxima
+++ b/Task/Trigonometric-functions/Maxima/trigonometric-functions.maxima
@ -0,0 +1,10 @@
+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;
--- a/Task/Trigonometric-functions/Metafont/trigonometric-functions.metafont
+++ b/Task/Trigonometric-functions/Metafont/trigonometric-functions.metafont
@ -0,0 +1,46 @@
+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
--- a/Task/Trigonometric-functions/NetRexx/trigonometric-functions.netrexx
+++ b/Task/Trigonometric-functions/NetRexx/trigonometric-functions.netrexx
@ -0,0 +1,35 @@
+/* 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
--- a/Task/Trigonometric-functions/OCaml/trigonometric-functions.ocaml
+++ b/Task/Trigonometric-functions/OCaml/trigonometric-functions.ocaml
@ -0,0 +1,14 @@
+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);;
--- a/Task/Trigonometric-functions/Octave/trigonometric-functions.octave
+++ b/Task/Trigonometric-functions/Octave/trigonometric-functions.octave
@ -0,0 +1,21 @@
+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
--- a/Task/Trigonometric-functions/Oz/trigonometric-functions.oz
+++ b/Task/Trigonometric-functions/Oz/trigonometric-functions.oz
@ -0,0 +1,21 @@
+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
--- a/Task/Trigonometric-functions/PARI-GP/trigonometric-functions.pari
+++ b/Task/Trigonometric-functions/PARI-GP/trigonometric-functions.pari
@ -0,0 +1,6 @@
+cos(Pi/2)
+sin(Pi/2)
+tan(Pi/2)
+acos(1)
+asin(1)
+atan(1)
--- a/Task/Trigonometric-functions/PHP/trigonometric-functions.php
+++ b/Task/Trigonometric-functions/PHP/trigonometric-functions.php
@ -0,0 +1,8 @@
+$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;
--- a/Task/Trigonometric-functions/PL-I/trigonometric-functions.pli
+++ b/Task/Trigonometric-functions/PL-I/trigonometric-functions.pli
@ -0,0 +1,18 @@
+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);
--- a/Task/Trigonometric-functions/PL-SQL/trigonometric-functions-1.sql
+++ b/Task/Trigonometric-functions/PL-SQL/trigonometric-functions-1.sql
@ -0,0 +1,12 @@
+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;
--- a/Task/Trigonometric-functions/PL-SQL/trigonometric-functions-2.sql
+++ b/Task/Trigonometric-functions/PL-SQL/trigonometric-functions-2.sql
@ -0,0 +1,4 @@
+ATAN2(n1,n2) --Arctangent(y/x), -pi < result <= +pi
+SINH(n) --Hyperbolic sine
+COSH(n) --Hyperbolic cosine
+TANH(n) --Hyperbolic tangent
--- a/Task/Trigonometric-functions/Pascal/trigonometric-functions.pascal
+++ b/Task/Trigonometric-functions/Pascal/trigonometric-functions.pascal
@ -0,0 +1,21 @@
+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.
--- a/Task/Trigonometric-functions/Perl-6/trigonometric-functions.pl6
+++ b/Task/Trigonometric-functions/Perl-6/trigonometric-functions.pl6
@ -0,0 +1,7 @@
+say sin(pi/3), ' ', sin 60, 'd'; # 'g' (gradians) and 1 (circles)
+say cos(pi/4), ' ', cos 45, 'd'; # are also recognized.
+say tan(pi/6), ' ', tan 30, 'd';
+
+say asin(sqrt(3)/2), ' ', asin sqrt(3)/2, 'd';
+say acos(1/sqrt 2),  ' ', acos 1/sqrt(2), 'd';
+say atan(1/sqrt 3),  ' ', atan 1/sqrt(3), 'd';
--- a/Task/Trigonometric-functions/Perl/trigonometric-functions.pl
+++ b/Task/Trigonometric-functions/Perl/trigonometric-functions.pl
@ -0,0 +1,17 @@
+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";
--- a/Task/Trigonometric-functions/PicoLisp/trigonometric-functions.l
+++ b/Task/Trigonometric-functions/PicoLisp/trigonometric-functions.l
@ -0,0 +1,20 @@
+(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) )
--- a/Task/Trigonometric-functions/Pop11/trigonometric-functions.pop11
+++ b/Task/Trigonometric-functions/Pop11/trigonometric-functions.pop11
@ -0,0 +1,15 @@
+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) =>
--- a/Task/Trigonometric-functions/PostScript/trigonometric-functions.ps
+++ b/Task/Trigonometric-functions/PostScript/trigonometric-functions.ps
@ -0,0 +1,11 @@
+90 sin =
+
+60 cos =
+
+%tan of 45 degrees
+
+45 sin 45 cos div =
+
+%inverse tan ( arc tan of sqrt 3)
+
+3 sqrt 1 atan =
--- a/Task/Trigonometric-functions/PowerShell/trigonometric-functions.psh
+++ b/Task/Trigonometric-functions/PowerShell/trigonometric-functions.psh
@ -0,0 +1,12 @@
+$rad = [Math]::PI / 4
+$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)
--- a/Task/Trigonometric-functions/PureBasic/trigonometric-functions.purebasic
+++ b/Task/Trigonometric-functions/PureBasic/trigonometric-functions.purebasic
@ -0,0 +1,24 @@
+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()
--- a/Task/Trigonometric-functions/Python/trigonometric-functions.py
+++ b/Task/Trigonometric-functions/Python/trigonometric-functions.py
@ -0,0 +1,20 @@
+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
+>>>
--- a/Task/Trigonometric-functions/R/trigonometric-functions.r
+++ b/Task/Trigonometric-functions/R/trigonometric-functions.r
@ -0,0 +1,23 @@
+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) ) )
--- a/Task/Trigonometric-functions/REBOL/trigonometric-functions.rebol
+++ b/Task/Trigonometric-functions/REBOL/trigonometric-functions.rebol
@ -0,0 +1,29 @@
+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]
--- a/Task/Trigonometric-functions/REXX/trigonometric-functions-1.rexx
+++ b/Task/Trigonometric-functions/REXX/trigonometric-functions-1.rexx
@ -0,0 +1,9 @@
+ ┌──────────────────────────────────────────────────────────────────────────┐
+ │  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.     │
+ └──────────────────────────────────────────────────────────────────────────┘
--- a/Task/Trigonometric-functions/REXX/trigonometric-functions-2.rexx
+++ b/Task/Trigonometric-functions/REXX/trigonometric-functions-2.rexx
@ -0,0 +1,109 @@
+/*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;   arg x;   if x<-1 | x>1 then call AsinErr;   s=x*x
+      if abs(x)>=.7 then return sign(x)*Acos(sqrt(1-s));  z=x;  o=x;  p=z
+      do j=2 by 2; o=o*s*(j-1)/j; z=z+o/(j+1); if z=p then leave; p=z; end
+      return z
+
+Atan: procedure; arg x; if abs(x)=1 then return pi()/4*sign(x)
+                                         return Asin(x/sqrt(1+x**2))
+
+cos: procedure; arg x; x=r2r(x); a=abs(x); numeric fuzz min(9,digits()-9)
+                if a=pi() then return -1;  if a=pi()/2 | a=2*pi() then return 0
+                if a=pi()/3 then return .5;  if a=2*pi()/3 then return -.5
+                return .sinCos(1,1,-1)
+
+sin: procedure; arg x;  x=r2r(x);  numeric fuzz min(5,digits()-3)
+                if abs(x)=pi() then return 0;   return .sinCos(x,x,1)
+
+.sinCos: parse arg z 1 p,_,i;  x=x*x
+         do k=2 by 2; _=-_*x/(k*(k+i));z=z+_;if z=p then leave;p=z;end; return z
+
+sqrt: procedure; parse arg x; if x=0 then return 0; d=digits();numeric digits 11
+      g=.sqrtGuess();       do j=0 while p>9;  m.j=p;  p=p%2+1;   end
+      do k=j+5 to 0 by -1; if m.k>11 then numeric digits m.k; g=.5*(g+x/g); end
+      numeric digits d;  return g/1
+.sqrtGuess: if x<0 then call sqrtErr;   numeric form;   m.=11;   p=d+d%4+2
+      parse value format(x,2,1,,0) 'E0' with g 'E' _ .;   return g*.5'E'_%2
+
+e: return,
+2.7182818284590452353602874713526624977572470936999595749669676277240766303535
+           /*Note:  the "real: E subroutine returns  E's  accuracy that */
+           /*matches the current NUMERIC DIGITS, up to 1 million digits.*/
+           /*If more than 1 million digits are required, be patient.    */
+
+exp: procedure; 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=z*e()**ix; return z
+
+pi: return,                            /*a bit of overkill,  but hey !! */
+3.1415926535897932384626433832795028841971693993751058209749445923078164062862
+           /*Note:  the real  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. */
+           /*If more than 1 million digits are required, be patient.    */
+
+Acos:  procedure; arg x; if x<-1|x>1 then call AcosErr; return .5*pi()-Asin(x)
+AcosD: return r2d(Acos(arg(1)))
+AsinD: return r2d(Asin(arg(1)))
+cosD:  return cos(d2r(arg(1)))
+sinD:  return sin(d2r(arg(1)))
+tan:   procedure; 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►1 unit circle*/
+d2r:   return r2r(arg(1)*pi()/180)     /*convert degrees ──► radians.   */
+r2d:   return d2d((arg(1)*180/pi()))   /*convert radians ──► degrees.   */
+r2r:   return arg(1)//(2*pi())         /*normalize radians►1 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
+sqrtErr: call tellErr "sqrt(x),  X  can't be negative,  X="||x
+  /*  ┌───────────────────────────────────────────────────────────────┐
+      │ Not included here are:  (among others):                       │
+      │ some of the usual higher-math functions normally associated   │
+      │  with trig functions:  POW, GAMMA, LGGAMMA, ERF, ERFC, ROOT,  │
+      │                        LOG (LN), LOG2, LOG10, ATAN2,          │
+      │ all of the hyperbolic trig functions and their inverses,      │
+      │                                    (too many to name here).   │
+      │ Angle conversions/normalizations: degrees/radians/grads/mils  │
+      │ [a circle = 2 pi radians, 360 degrees, 400 grads,  6400 mils].│
+      │ Some of the other trig functions (hypens added intentially):  │
+      │  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 vercosine)                            │
+      │  VSN  (versed sine   or versine)                              │
+      │  XCS  (exsecant)                                              │
+      │  COS/SIN/TAN cardinal  (damped  COS/SIN/TAN  function)        │
+      │  COS/SIN     integral                                         │
+      │    and all pertinent of the above's inverses (AVSN, ACVS...)  │
+      └───────────────────────────────────────────────────────────────┘ */
--- a/Task/Trigonometric-functions/RapidQ/trigonometric-functions.rapidq
+++ b/Task/Trigonometric-functions/RapidQ/trigonometric-functions.rapidq
@ -0,0 +1,33 @@
+$APPTYPE CONSOLE
+$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
--- a/Task/Trigonometric-functions/Ruby/trigonometric-functions-1.rb
+++ b/Task/Trigonometric-functions/Ruby/trigonometric-functions-1.rb
@ -0,0 +1,26 @@
+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)}"
--- a/Task/Trigonometric-functions/Ruby/trigonometric-functions-2.rb
+++ b/Task/Trigonometric-functions/Ruby/trigonometric-functions-2.rb
@ -0,0 +1,63 @@
+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")
--- a/Task/Trigonometric-functions/Run-BASIC/trigonometric-functions.run
+++ b/Task/Trigonometric-functions/Run-BASIC/trigonometric-functions.run
@ -0,0 +1,13 @@
+deg = 45.0
+' Run BASIC works in radians. Convert deg and rad as shown.
+d2r = ACS(-1)/180
+rad = deg*d2r
+r2d = 180/ACS(-1)
+
+print "Sine:        ";SIN(rad);"     ";SIN(deg*d2r)
+print "Cosine:      ";COS(rad);"     ";COS(deg*d2r)
+print "Tangent:     ";TAN(rad);"      ";TAN(deg*d2r)
+print
+print "Arcsine:     ";ASN(SIN(rad));" radians, (or ";ASN(SIN(deg*d2r))*r2d;" degrees)"
+print "Arccosine:   ";ACS(COS(rad));" radians, (or ";ACS(COS(deg*d2r))*r2d;" degrees)"
+print "Arctangent:  ";ATN(TAN(rad));" radians, (or ";ATN(TAN(deg*d2r))*r2d;" degrees)"
--- a/Task/Trigonometric-functions/SAS/trigonometric-functions.sas
+++ b/Task/Trigonometric-functions/SAS/trigonometric-functions.sas
@ -0,0 +1,31 @@
+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;
--- a/Task/Trigonometric-functions/Scheme/trigonometric-functions.ss
+++ b/Task/Trigonometric-functions/Scheme/trigonometric-functions.ss
@ -0,0 +1,37 @@
+(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)
--- a/Task/Trigonometric-functions/Seed7/trigonometric-functions.seed7
+++ b/Task/Trigonometric-functions/Seed7/trigonometric-functions.seed7
@ -0,0 +1,17 @@
+$ 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;
--- a/Task/Trigonometric-functions/Tcl/trigonometric-functions.tcl
+++ b/Task/Trigonometric-functions/Tcl/trigonometric-functions.tcl
@ -0,0 +1,18 @@
+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
--- a/Task/Trigonometric-functions/XPL0/trigonometric-functions.xpl0
+++ b/Task/Trigonometric-functions/XPL0/trigonometric-functions.xpl0
@ -0,0 +1,27 @@
+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);
+]
				`@ -0,0 +1 @@`
				`math:cos(Deg * math:pi() / 180)==math:cos(Rad).`
				`@ -0,0 +1 @@`
				`math:tan(Deg * math:pi() / 180)==math:tan(Rad).`
				`@ -0,0 +1 @@`
				`>,:(1&o. ; 2&o. ; 3&o.) (4%~o. 1), 180%~o. 45`
				`@ -0,0 +1 @@`
				`>,:([ , 180p_1&*)&.> (_1&o. ; _2&o. ; _3&o.) 0.5`
				`@ -0,0 +1 @@`
				`print(math.cos(1), math.sin(1), math.tan(1), math.atan(1), math.atan2(3, 4))`