直角三角函数，求直角三角函数的全部公式

1.诱导公式

sin(-a) = - sin(a)

cos(-a) = cos(a)

sin(π/2 - a) = cos(a)

cos(π/2 - a) = sin(a)

sin(π/2 + a) = cos(a)

cos(π/2 + 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 - b) = /

3.

和差化积公式

sin(a) + sin(b) = 2sincos

sin(a) sin(b) = 2cossin

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

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

4.

积化和差公式

sin(a)sin(b) = - 1/2

cos(a)cos(b) = 1/2

sin(a)cos(b) = 1/2

5.

二倍角公式

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

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

6.

半角公式

sin2(a/2) = / 2

cos2(a/2) = / 2

tan(a/2) = /sin(a) = sina /

7.万能公式

sin(a) = 2tan(a/2) /

cos(a) = /

tan(a) = 2tan(a/2) /