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삼각함수의 정리

삼각함수의 정리

덧셈정리

sin(x + y) = sin(x) * cos(y) + cos(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)
cos(x - y) = cos(x) * cos(y) + sin(x) * sin(y)
tan(x + y) = (tan(x) + tan(y)) / (1 - tan(x) * tan(y))
tan(x - y) = (tan(x) - tan(y)) / (1 + tan(x) * tan(y))


배각정리

sin(2 * x) = 2 * sin(x) * cos(x)
cos(2 * x) = cos²(x) - sin²(x) = 2 * cos²(x) - 1 = 1 - 2 * sin²(x)
tan(2 * x) = (2 * tan(x)) / (1 - tan²(x))


반각의 정리

sin²(x / 2) = (1 - cos(x)) / 2
cos²(x / 2) = (1 + cos(x)) / 2
tan²(x / 2) = (1 - cos(x)) / (1 + cos(x))


삼각함수 공식 총괄정리

sin(-θ)=-sinθ, cos(-θ)=cosθ, tan(-θ)=-tanθ
sin²θ+cos²θ=1, sec²θ-tan²θ=1, csc²θ-cot²θ=1
sin(π/2-θ)=cosθ, sin(π/2+θ)=cosθ, sin(θ±π/2)=±cosθ
cos(π/2-θ)=sinθ, cos(π/2+θ)=-sinθ, cos(θ±π/2)=Ŧsinθ
sin(π-θ)=sinθ, sin(π+θ)=-sinθ, sin(θ±π)=-sinθ
cos(π-θ)=-cosθ, cos(π+θ)=-cosθ, cos(θ±π)=-cosθ
sin(α±β)=sinαcosβ±cosαsinβ, cos(α±β)=cosαcosβŦsinαsinβ
tan(α+β)=tanα+tanβ/1-tanαtanβ, tan(α-β)=tanα-tanβ/1+tanαtanβ
sin2θ=2sinθcosθ
cos2θ=cos²θ-sin²θ=2cos²θ-1=1-2sin²θ, tan2θ=2tanθ/1-tan²θ
sin²θ/2=1-cosθ/2, cos²θ/2=1+cosθ/2, tan²θ/2=1-cosθ/1+cosθ
sinαcosβ=1/2{sin(α+β)+sin(α-β)}
cosαcosβ=1/2{cos(α+β)+cos(α-β)}
sinαsinβ=-1/2{cos(α+β)-cos(α-β)}
sinα+sinβ=2sin(α+β/2)cos(α-β/2)
sinα-sinβ=2cos(α+β/2)sin(α-β/2)
cosα+cosβ=2cos(α+β/2)cos(α-β/2)
cosα-cosβ=-2sin(α+β/2)sin(α-β/2)

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