#!/usr/koeki/bin/ruby

require 'mathn'

def fac(m)
  if m == 1
    1
  else
    m * fac(m-1)
  end
end

def sin_taylor1(x, m)
  x 
end

def sin_taylor2(x, m)
  x - 1/fac(m) * x ** m 
end

def sin_taylor3(x, m)
  x - 1/fac(m-2) * x ** (m-2) + 1/fac(m) * x ** m
end

def sin_taylor4(x, m)
  x  - 1/fac(m-4) * x ** (m-4) + 1/fac(m-2) * x ** (m-2) - 1/fac(m) * x ** m
end

n = 5

printf("%-2s %10s %10s %8s %8s %8s %8s %8s %8s %8s",
       "¡ë","Àµ¸¹ÃÍ",
       "Ÿ³«1¼¡","Ÿ³«2¼¡","Ÿ³«3¼¡","Ÿ³«4¼¡",
       "º¹Ê¬¤Î2¾è","º¹Ê¬¤Î2¾è", "º¹Ê¬¤Î2¾è", "º¹Ê¬¤Î2¾è")
for i in 0..8
  puts ""
  for theta in i * 10 + 0..i * 10 + 9
    rad = Math::PI * theta/180
    sine = Math.sin(rad)
    taylor1 = sin_taylor1(rad,1)
    taylor2 = sin_taylor2(rad,3)
    taylor3 = sin_taylor3(rad,5)
    taylor4 = sin_taylor4(rad,7)
    printf("%2d | %8.6f | %8.6f %8.6f %8.6f %8.6f | %8.1e %8.1e %8.1e %8.1e\n", 
	   theta, sine, 
	   taylor1, taylor2, taylor3, taylor4,
	   (sine-taylor1) ** 2, 
	   (sine-taylor2) ** 2, 
	   (sine-taylor3) ** 2, 
	   (sine-taylor4) ** 2)
  end

end