To: J3                                                     J3/19-145
From: Lorri Menard
Subject: Degree trigonometric functions
Date: 2019-February-12
Reference:  m215/18-139r1, m217/18-272r1

1 Introduction

Addition of the degree trigonometric functions was approved for further
work at m217.  This paper attempts to craft specifications.

2 Specifications

These intrinsics are elemental and generic.   All would be similar to
their radix counterparts except that the argument(s) or return values
would be in degrees.

3 Syntax

    ACOSD produces the arccosine of X.

    result = ACOSD (X)
      X    (Input) Must be of type real.
           The | X | must be less than or equal to 1.

The result type and kind are the same as X and are expressed in degrees.
The value lies in the range -90 to 90 degrees.

     ASIND produces the arcsine of X.

     result = ASIND (X)
      X    (Input) Must be of type real.
           The | X | must be less than or equal to 1.

The result type and kind are the same as X and are expressed in degrees.
The value lies in the range -90 to 90 degrees.

     ATAND produces the arctangent of X.

     result = ATAND (X)
      X    (Input) Must be of type real and must be greater than or
           equal to zero.

The result type and kind are the same as X and are expressed in degrees.

     ATAN2D produces an arctangent. The result is the principal value of
     the argument of the nonzero complex number (X, Y).

     result = ATAN2D (Y,X)

     Y     (Input) Must be of type real.
     X     (Input) Must have the same type and kind parameters as Y.
           If Y has the value zero, X cannot have the value zero.

The result type and kind are the same as X and are expressed in degrees.
The value lies in the range -180 degrees to 180 degrees. If X zero, the
result is approximately equal to the value of arctan (Y/X).

    If Y > zero, the result is positive.

    If Y < zero, the result is negative.

    If Y = zero, the result is zero (if X > zero) or
                 180 degrees (if X < zero).

    If X = zero, the absolute value of the result is 90 degrees.


    COSD produces the cosine of X.

    result = COSD(X)

    X      (Input) Must be of type real. It must be in degrees and is
           treated as modulo 360.

The result type and kind are the same as X.

4 Edits
   To be supplied later
    SIND produces the sind of X.

    result = SIND(X)

    X      (Input) Must be of type real. It must be in degrees and is
           treated as modulo 360.

The result type and kind are the same as X.

    TAND produces the tangent of X

    result = TAND(X)

    X      (Input) Must be of type real. It must be in degrees and is
           treated as modulo 360.

The result type and kind are the same as X.