文科数学中所有的公式

Question

如题所述

Answer 1

1.诱导公式
sin(-a)=-sin(a)
cos(-a)=cos(a)
sin(π2-a)=cos(a)
cos(π2-a)=sin(a)
sin(π2
a)=cos(a)
cos(π2
a)=-sin(a)
sin(π-a)=sin(a)
cos(π-a)=-cos(a)
sin(π
a)=-sin(a)
cos(π
a)=-cos(a)
2.两角和与差的三角函数
sin(a
b)=sin(a)cos(b)
cos(α)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)1-tan(a)tan(b)
tan(a-b)=tan(a)-tan(b)1
tan(a)tan(b)
3.和差化积公式
sin(a)
sin(b)=2sin(a
b2)cos(a-b2)
sin(a)−sin(b)=2cos(a
b2)sin(a-b2)
cos(a)
cos(b)=2cos(a
b2)cos(a-b2)
cos(a)-cos(b)=-2sin(a
b2)sin(a-b2)
4.二倍角公式
sin(2a)=2sin(a)cos(b)
cos(2a)=cos2(a)-sin2(a)=2cos2(a)-1=1-2sin2(a)
5.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)
6.万能公式
sin(a)=2tan(a2)1
tan2(a2)
cos(a)=1-tan2(a2)1
tan2(a2)
tan(a)=2tan(a2)1-tan2(a2)
7.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