The trigonometric function induction formula is a mathematical formula, which refers to the formula that transforms a trigonometric function with a large angle into a trigonometric function with a small angle through periodicity. There are six groups of formulas, 54 * * *.

The trigonometric function induction formula is to transform the trigonometric function of angle n (π/2) α into the trigonometric function of angle α, including some commonly used formulas and differential product formulas.

Equation 5: Using Equation 1 and Equation 3, we can get the relationship between the trigonometric function values of 2π-α and α:

sin(2π-α)=-sinα； cos(2π-α)= cosα；

tan(2π-α)=-tanα； cot(2π-α)=-cotα；

Equation 6: the relationship between π/2α and the trigonometric function value of α;

1, π/2+α and the trigonometric function value of α;

Representation of angles in arc system;

sin(π/2+α)= cosα； cos(π/2+α)=—sinα；

tan(π/2+α)=-cotα； cot(π/2+α)=-tanα；

sec(π/2+α)=-CSCα； CSC(π/2+α)= secα；

Representation of angle in angle system;

sin(90+α)= cosα； cos(90+α)=-sinα；

tan(90+α)=-cotα； cot(90+α)=-tanα；

sec(90+α)=-CSCα； CSC(90+α)= secα；

2. The relationship between π/2-α and the trigonometric function value of α:

Representation of angles in arc system;

sin(π/2-α)= cosα； cos(π/2-α)= sinα；

tan(π/2-α)= cotα； cot(π/2-α)= tanα；

sec(π/2-α)= CSCα； CSC(π/2-α)= secα；

Representation of angle in angle system;

sin(90-α)= cosα； cos(90-α)= sinα；

tan(90-α)= cotα； cot(90-α)= tanα；

sec(90-α)= CSCα； CSC(90-α)= secα；

3.3π/2+α and the trigonometric function value of α

Representation of angles in arc system;

sin(3π/2+α)=-cosα； cos(3π/2+α)= sinα；

tan(3π/2+α)=-cotα； cot(3π/2+α)=-tanα；

sec(3π/2+α)= CSCα； CSC(3π/2+α)=-secα；

Representation of angle in angle system;

sin(270+α)=-cosα； cos(270+α)= sinα；

tan(270+α)=-cotα； cot(270+α)=-tanα；

sec(270+α)= CSCα；

CSC(270+α)=-secα；

4.3 the relationship between π/2-α and the trigonometric function value of α:

Representation of angles in arc system;

sin(3π/2-α)=-cosα； cos(3π/2-α)=-sinα；

tan(3π/2-α)= cotα； cot(3π/2-α)= tanα；

sec(3π/2-α)=-CSCα； CSC(3π/2-α)=-secα；

Representation of angle in angle system;

sin(270-α)=-cosα； cos(270-α)=-sinα；

tan(270-α)= cotα； cot(270-α)= tanα；

sec(270-α)=-CSCα； CSC(270-α)=- second α.