正弦余弦公式

1.诱导公式

sin(-a)=-sin(a)

cos(-a)=cos(a)

sin(2π-a)=cos(a)

cos(2π-a)=sin(a)

sin(2π+a)=cos(a)

cos(2π+a)=-sin(a)

sin(π-a)=sin(a)

cos(π-a)=-cos(a)

sin(π+a)=-sin(a)

cos(π+a)=-cos(a)

tgA=tanA=sinAcosA

2.两角和与差的三角函数

sin(a+b)=sin(a)cos(b)+cos(a)sin(b)

cos(a+b)=cos(a)cos(b)-sin(a)sin(b)

sin(a-b)=sin(a)cos(b)-cos(a)sin(b)

cos(a-b)=cos(a)cos(b)+sin(a)sin(b)

tan(a+b)=tan(a)+tan(b)-tan(a)tan(b)

tan(a-b)=tan(a)-tan(b)+tan(a)tan(b)

3.和差化积公式

sin(a)+sin(b)=2sin(a+b)cos(a-b)

sin(a)·sin(b)=2cos(a+b)sin(a-b)

cos(a)+cos(b)=2cos(a+b)cos(a-b)

cos(a)-cos(b)=-2sin(a+b)sin(a-b)

4.积化和差公式

sin(a)sin(b)=-12·[cos(a+b)-cos(a-b)]

cos(a)cos(b)=12·[cos(a+b)+cos(a-b)]

sin(a)cos(b)=12·[sin(a+b)+sin(a-b)]

5.二倍角公式

sin(2a)=2sin(a)cos(a)

cos(2a)=cos2(a)-sin2(a)=2cos2(a)-1=1-2sin2(a)

6.半角公式

sin2(a2)=1-cos(a)2

cos2(a2)=1+cos(a)2

tan(a2)=1-cos(a)sin(a)=sina1+cos(a)

7.万能公式

sin(a)=2tan(a2)1+tan2(a2)

cos(a)=1-tan2(a2)1+tan2(a2)

tan(a)=2tan(a2)1-tan2(a2)

8.其它公式(推导出来的 )

a·sin(a)+b·cos(a)=a2+b2sin(a+c) 其中 tan(c)=ba

a·sin(a)-b·cos(a)=a2+b2cos(a-c) 其中 tan(c)=ab

1+sin(a)=(sin(a2)+cos(a2))2

1-sin(a)=(sin(a2)-cos(a2))2

csc(a)=1sin(a)

sec(a)=1cos(a)