Problem Statement

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

Let's start with the solution:

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


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


   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