share/trigonometry/spangl.mac

   1 /* -*- Mode: MACSYMA; BASE: 10 -*- */
   2 matchdeclare(greater1,greater1p,onetofour,onetofourp)$
   3 greater1p(n):=ratnump(n) and n>1$
   4 onetofourp(n):=greater1p(n) and n<4$
   5
   6 tellsimp(sin(2*greater1*%pi),sin(leastremainder(2*greater1,2)*%pi))$
   7 tellsimp(cos(2*greater1*%pi),cos(leastremainder(2*greater1,2)*%pi))$
   8 tellsimp(csc(2*greater1*%pi),csc(leastremainder(2*greater1,2)*%pi))$
   9 tellsimp(sec(2*greater1*%pi),sec(leastremainder(2*greater1,2)*%pi))$
  10 tellsimp(tan(greater1*%pi),tan(leastremainder(greater1,1)*%pi))$
  11 tellsimp(cot(greater1*%pi),cot(leastremainder(greater1,1)*%pi))$
  12
  13 leastremainder(dividend,divisor):=dividend-divisor*entier(dividend/divisor+1/2)$
  14
  15 tellsimp(sin(onetofour*%pi),-sin((onetofour-1)*%pi))$
  16 tellsimp(cos(onetofour*%pi),-cos((onetofour-1)*%pi))$
  17 tellsimp(csc(onetofour*%pi),-csc((onetofour-1)*%pi))$
  18 tellsimp(sec(onetofour*%pi),-sec((onetofour-1)*%pi))$
  19
  20 tellsimp(sin(onetofour*%pi/4),cos((1/2-onetofour/4)*%pi))$
  21 tellsimp(cos(onetofour*%pi/4),sin((1/2-onetofour/4)*%pi))$
  22 tellsimp(csc(onetofour*%pi/4),sec((1/2-onetofour/4)*%pi))$
  23 tellsimp(sec(onetofour*%pi/4),csc((1/2-onetofour/4)*%pi))$
  24 tellsimp(tan(onetofour*%pi/4),cot((1/2-onetofour/4)*%pi))$
  25 tellsimp(cot(onetofour*%pi/4),tan((1/2-onetofour/4)*%pi))$
  26
  27 tellsimpafter(sin(%pi/10),(%phi-1)/2)$
  28 tellsimpafter(cos(%pi/5),%phi/2)$
  29 tellsimpafter(csc(%pi/10),2*%phi)$
  30 tellsimpafter(sec(%pi/5),2*(%phi-1))$
  31
  32 tellsimpafter(sin(%pi/12),(sqrt(6)-sqrt(2))/4)$
  33 tellsimpafter(cos(%pi/12),(sqrt(6)+sqrt(2))/4)$
  34 tellsimpafter(csc(%pi/12),sqrt(6)+sqrt(2))$
  35 tellsimpafter(sec(%pi/12),sqrt(6)-sqrt(2))$
  36
  37 tellsimpafter(tan(%pi/8),sqrt(2)-1)$
  38 tellsimpafter(cot(%pi/8),sqrt(2)+1)$
  39
  40 tellsimpafter(tan(%pi/12),2-sqrt(3))$
  41 tellsimpafter(cot(%pi/12),2+sqrt(3))$
  42 tellsimpafter(tan(%pi/24),(sqrt(3)-sqrt(2))*(sqrt(2)-1))$
  43 tellsimpafter(cot(%pi/24),(sqrt(3)+sqrt(2))*(sqrt(2)+1))$
  44 tellsimpafter(tan(5*%pi/24),(sqrt(3)-sqrt(2))*(sqrt(2)+1))$
  45 tellsimpafter(cot(5*%pi/24),(sqrt(3)+sqrt(2))*(sqrt(2)-1))$