三角函式轉換公式

1、誘導公式：sin(-α)

= -sinα；cos(-α) = cosα；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

2、兩角和差公式：

sin(AB) = sinAcosBcosAsinB

cos(AB) = cosAcosBsinAsinB

tan(AB) = (tanAtanB)/(1tanAtanB)

cot(AB) = (cotAcotB1)/(cotBcotA) 3、倍角公式sin2A=2sinA•cosA

cos2A=cosA2-sinA2=1-2sinA2=2cosA2-1

tan2A=2tanA/（1-tanA2）=2cotA/(cotA2-1)4、半形公式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))

5、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)

6、積化和差sinαsinβ

= -1/2*[cos(α-β)-cos(α+β)]

cosαcosβ =

1/2*[cos(α+β)+cos(α-β)]

sinαcosβ =

1/2*[sin(α+β)+sin(α-β)]

cosαsinβ = 1/2*[sin(α+β)-sin(α-β)]萬能公式