三角函數公式大全(2)

半角公式

tan(A/2)=(1-cosA)/sinA=sinA/(1+cosA);

cot(A/2)=sinA/(1-cosA)=(1+cosA)/sinA.

sin^2(a/2)=(1-cos(a))/2

cos^2(a/2)=(1+cos(a))/2

tan(a/2)=(1-cos(a))/sin(a)=sin(a)/(1+cos(a))

三角和

sin(α+β+γ)=sinα·cosβ·cosγ+cosα·sinβ·cosγ+cosα·cosβ·sinγ-sinα·sinβ·sinγ

cos(α+β+γ)=cosα·cosβ·cosγ-cosα·sinβ·sinγ-sinα·cosβ·sinγ-sinα·sinβ·cosγ

tan(α+β+γ)=(tanα+tanβ+tanγ-tanα·tanβ·tanγ)/(1-tanα·tanβ-tanβ·tanγ-tanγ·tanα)

兩角和差

cos(α+β)=cosα·cosβ-sinα·sinβ

cos(α-β)=cosα·cosβ+sinα·sinβ

sin(α±β)=sinα·cosβ±cosα·sinβ

tan(α+β)=(tanα+tanβ)/(1-tanα·tanβ)

tan(α-β)=(tanα-tanβ)/(1+tanα·tanβ)

和差化積

sinθ+sinφ = 2 sin[(θ+φ)/2] cos[(θ-φ)/2]

sinθ-sinφ = 2 cos[(θ+φ)/2] sin[(θ-φ)/2]

cosθ+cosφ = 2 cos[(θ+φ)/2] cos[(θ-φ)/2]

cosθ-cosφ = -2 sin[(θ+φ)/2] sin[(θ-φ)/2]

tanA+tanB=sin(A+B)/cosAcosB=tan(A+B)(1-tanAtanB)

tanA-tanB=sin(A-B)/cosAcosB=tan(A-B)(1+tanAtanB)

積化和差

sinαsinβ = [cos(α-β)-cos(α+β)] /2

cosαcosβ = [cos(α+β)+cos(α-β)]/2

sinαcosβ = [sin(α+β)+sin(α-β)]/2

cosαsinβ = [sin(α+β)-sin(α-β)]/2

誘導公式

sin(-α) = -sinα

cos(-α) = cosα

tan (—a)=-tanα

sin(π/2-α) = cosα

cos(π/2-α) = sinα

sin(π/2+α) = cosα

cos(π/2+α) = -sinα

sin(π-α) = sinα

cos(π-α) = -cosα

sin(π+α) = -sinα

cos(π+α) = -cosα

tanA= sinA/cosA

tan(π/2+α)=-cotα

tan(π/2-α)=cotα

tan(π-α)=-tanα

tan(π+α)=tanα