=begin
=Formulas for Trigonometric Functions
三角関数公式
==一般的な関係式
*sin(-x) = -sin(x)
*cos(-x) = cos(x)
*sin(π/2 -x) = cos(x)
*sin(π-x) = sin(x)
*cos(π/2 -x) = sin(x)
*cos(π-x) = -cos(x)
*sin(π/2 +x) = cos(x)
*sin(π+x) = -sin(x)
*cos(π/2 +x) = -sin(x)
*cos(π+x) = -cos(x)
*sin(x)2 + cos(x)2 = 1
==加法定理
*sin(x+y) = sin(x)cos(y) + cos(x)sin(y)
*cos(x+y) = cos(x)cos(y) - sin(x)sin(y)
*sin(x-y) = sin(x)cos(y) - cos(x)sin(y)
*cos(x-y) = cos(x)cos(y) + sin(x)sin(y)
==積和公式
*2sin(x)cos(y) = sin(x+y) + sin(x-y)
*2cos(x)sin(y) = sin(x+y) - sin(x-y)
*2cos(x)cos(y) = cos(x+y) + cos(x-y)
*2sin(x)sin(y) = -cos(x+y) + cos(x-y)
==和積公式
*sin(x) + sin(y) = 2sin( (x+y)/2 )・ cos( (x-y)/2 )
*sin(x) - sin(y) = 2cos( (x+y)/2 )・ sin( (x-y)/2 )
*cos(x) + cos(y) = 2cos( (x+y)/2 )・ cos( (x-y)/2 )
*cos(x) - cos(y) = -2sin( (x+y)/2 )・ sin( (x-y)/2 )
==倍角公式
*sin(2x) = 2sin(x)cos(x)
*cos(2x) = cos(x)2 - sin(x)2 = 2cos(x)2 - 1 = 1 - 2sin(x)2
==半角公式
*sin(x/2)2 = ( 1-cos(x) )/2
*cos(x/2)2 = ( 1+cos(x) )/2
==複素
*ei x = cos(x) + i sin(x)
*ei (x+y) = ei x ei y
==リンク
この式集は ((<三角関数資料|URL:http://hp.vector.co.jp/authors/VA003604/sincos.htm>))
を参考に整理した(殆どそのままである)。感謝
*三角関数資料 URL:http://hp.vector.co.jp/authors/VA003604/sincos.htm
==letters
• π · ± ⋅ ² ³ × ÷ ℑ ℘ ℜ ℵ ∞
=end
=begin
==rdソース
(())
ruby -pe 'gsub("<","<").gsub!(">",">")'
=end