SAT tends to be an intelligence test, which is also very obvious in SAT math exam. The content of the exam is not entirely mathematical knowledge itself. What I want to share with you is the formula of complex variable function in SAT mathematics.

1. inductive formula

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. The trigonometric function of the sum and difference of two angles

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. Sum-difference product formula

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

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

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