share/trigonometry/ntrig.mac

   1 eval_when([translate,batch,demo,load,loadfile],
   2 matchdeclare(n,integerp))$
   3
   4 tellsimpafter(sin(n*%pi/10),usin(n))$
   5 tellsimpafter(cos(n*%pi/10),ucos(n))$
   6 tellsimpafter(tan(n*%pi/10),usin(n)/ucos(n))$
   7 tellsimpafter(cot(n*%pi/10),ucos(n)/usin(n))$
   8 tellsimpafter(sec(n*%pi/10),1/ucos(n))$
   9 tellsimpafter(csc(n*%pi/10),1/usin(n))$
  10
  11 usin(n):= block([yuk:remainder(remainder(n,10)+10,10),
  12                  sgn:if remainder(remainder(n,20)+20,20)>=10 then -1 else 1],
  13 if yuk=1 or yuk=9 then sgn*(sqrt(5)-1)/4 else
  14 if yuk=2 or yuk=8 then sgn*(sqrt(5)-1)*sqrt(sqrt(5)+5)/(4*sqrt(2)) else
  15 if yuk=3 or yuk=7 then sgn*(sqrt(5)+1)/4 else
  16 if yuk=4 or yuk=6 then sgn*sqrt(sqrt(5)+5)/(2*sqrt(2)))$
  17
  18 ucos(n):= block([yuk:remainder(remainder(n,10)+10,10),
  19                  sgn:if remainder(remainder(n,20)+20,20)>5 and
  20                         remainder(remainder(n,20)+20,20)<15 then -1 else 1],
  21 if yuk=1 or yuk=9 then sgn*sqrt(sqrt(5)+5)/(2*sqrt(2)) else
  22 if yuk=2 or yuk=8 then sgn*(sqrt(5)+1)/4 else
  23 if yuk=3 or yuk=7 then sgn*(sqrt(5)-1)*sqrt(sqrt(5)+5)/(4*sqrt(2)) else
  24 if yuk=4 or yuk=6 then sgn*(sqrt(5)-1)/4)$