share/trigonometry/atrig1.mac

   1 /* -*-Macsyma-*- */
   2 eval_when(batch,ttyoff:true)$
   3 /*SHARE1;ATRIG1 1
   4 12:01am  Friday, 14 January 1983
   5   Created.
   6 */
   7
   8 eval_when(translate,
   9           transcompile:true,
  10           define_variable:'mode)$
  11
  12 put('atrig1,1,'version)$
  13
  14 /* Variable definitions */
  15
  16 define_variable(piover4,%pi/4,any)$
  17 define_variable(piover3,%pi/3,any)$
  18 define_variable(piover6,%pi/6,any)$
  19 define_variable(piover8,%pi/8,any)$
  20 define_variable(sqrt3,sqrt(3),any)$
  21 define_variable(sqrt2,sqrt(2),any)$
  22 define_variable(angles_known_for_atrig,[0,piover6,piover4,piover3,%pi/2],
  23                 any)$
  24
  25 /* For %PI/4 */
  26
  27 tellsimpafter(acos(1/sqrt2),piover4)$
  28 tellsimpafter(acos(sqrt2/2),piover4)$
  29 tellsimpafter(asec(sqrt2),piover4)$
  30 tellsimpafter(acsc(sqrt2),piover4)$
  31 tellsimpafter(asin(1/sqrt2),piover4)$
  32 tellsimpafter(asin(sqrt2/2),piover4)$
  33
  34 /* For %PI/3 */
  35
  36 tellsimpafter(asin(sqrt3/2),piover3)$
  37 tellsimpafter(atan(sqrt3),  piover3)$
  38 tellsimpafter(acot(1/sqrt3),piover3)$
  39 tellsimpafter(acot(sqrt3/3),piover3)$
  40 tellsimpafter(acsc(2*sqrt3/3),piover3)$
  41 tellsimpafter(acsc(2/sqrt3),piover3)$
  42 tellsimpafter(asec(2),piover3)$
  43
  44 /* For %PI/6 */
  45
  46 tellsimpafter(acos(sqrt3/2),piover6)$
  47 tellsimpafter(atan(sqrt3/3),piover6)$
  48 tellsimpafter(atan(1/sqrt3),piover6)$
  49 tellsimpafter(acot(sqrt3),  piover6)$
  50 tellsimpafter(asec(2/sqrt3),piover6)$
  51 tellsimpafter(asec(2*sqrt3/3),piover6)$
  52 tellsimpafter(acsc(2),        piover6)$
  53
  54 /* For %PI/8 */
  55
  56 tellsimpafter(atan(sqrt2-1),piover8)$
  57 tellsimpafter(atan(sqrt2+1),3*piover8)$
  58
  59 /* Could also do  [1,5,7,11]*%PI/12 if there is ever demand for it. */
  60
  61 eval_when(batch,ttyoff:false)$
  62