三角形

基本法則

1.sin²θ+cos²θ=1

2.sinθ=cos(90^o-θ)

3.tanθ=sinθ/cosθ

4.tanθ=1/tan(90^o-θ)

半角三角函數

5.sinθ=2sin(θ/2)cos(θ/2)

6.cosθ=1-2sin²(θ/2)

7.sin(θ/2)=±√½(1-cosθ)

8.cos(θ/2)=±√½(1+cosθ)

9.tan(θ/2)=±√(1-cosθ)/(1+cosθ)

           =1-cosθ/sinθ

           =sinθ/(1+cosθ)

和積互變公式

10.(sinx)(cosy)=½[sin(x+y)+sin(x-y)]

11.(cosx)(siny)=½[sin(x+y)-sin(x-y)]

12.(cosx)(cosy)=½[cos(x+y)+cos(x-y)]

13.(sinx)(siny)=-½[cos(x+y)-cos(x-y)]

和差化積公式(任意角a, b)

14.sina+sinb=2sin[½(a+b)]cos[½(a-b)]

15.sina-sinb=2cos[½(a+b)]sin[½(a-b)]

16.cosa+cosb=2cos[½(a+b)]cos[½(a-b)]

17.cosa-cosb=-2sin[½(a+b)]sin[½(a-b)]

二倍角公式

18.sin2A=2sinAcosA

19.cos2A=cos²A-sin²A

20.tan2A=2tanA/(1-tan²A)

三倍角公式

21.sin3A=3sinA-4sin³A

22.cos3A=4cos³-3cosA

23.tan3A=(3tanA-tan³A)/(1-3tan²A)

兩角和差的三角函數

24.sin(A+B)=sinAcosB+cosAsinB

25.sin(A-B)=sinAcosB-cosAsinB

26.cos(A+B)=cosAcosB-sinAsinB

27.cos(A-B)=cosAcosB+sinAsinB

28.tan(A+B)=(tanA+tanB)/(1-tanAtanB)

29.tan(A-B)=(tanA-tanB)/(1+tanAtanB)

三角和的三角函數

30.sin(A+B+C)=sinAcosBcosC+cosAsinBcosC+cosAcosBsinC-sinAsinBsinC

31.cos(A+B+C)=cosAcosBcosC-cosAsinBsinC-sinAcosBsinC-sinAsinBcosC

32.tan(A+B+C)=(tanA+tanB+tanC-tanAtanBtanC)/(1-tanAtanB-tanBtanC-tanAtanC)

特別的積商公式

33.sin(A+B)sin(A-B)=sin²A-sin²B

34.cos(A+B)cos(A-B)=cos²A-sin²B=cos²B-sin²A

35.[sin(A+B)]/[sin(A-B)]=(tanA+tanB)/(tanA-tanB)