三角函数诱导公式1-6
三角函数导数诱导公式？
三角函数导数诱导公式？
常用三角函数的导数公式大全
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(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.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
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)