I. Definition

Formulas of trigonometric functions is a function formula of transcendental function in elementary function in mathematics. Their essence is the mapping between the set of arbitrary angles and a set of ratio variables, and the usual trigonometric functions are defined in the plane rectangular coordinate system.

Second, the inductive formula

1. Formula 1: Let α be any angle, and the values of the same trigonometric function of the angles with the same terminal edges are equal.

2. Formula 2: Let α be an arbitrary angle, and the relationship between the trigonometric function value of π+α and the trigonometric function value of α.

sin(π+α)？ =? -sinα，cos(π+α)=-cosα，tan(π+α)=？ tanα，cot(π+α)=cotα

3. Formula 3: Relationship between any angle α and trigonometric function value of-α.

sin(-α)=-sinα，cos(-α)=cosα，tan(-α)=-tanα，cot(-α)=-cotα

4.？ Formula 4: The relationship between π-α and the trigonometric function value of α can be obtained by using Formula 2 and Formula 3.

sin(π-α)=sinα，cos(π-α)=-cosα，tan(π-α)=-tanα，cot(π-α)=-cotα

5. Formula 5: Using Formula 1 and Formula 3, the relationship between the trigonometric function values of 2π-α and α can be obtained.

sin(2π-α)=-sinα，cos(2π-α)=cosα，tan(2π-α)=-tanα，cot(2π-α)=-cotα

Memory tip: the odd number remains the same, and the symbol looks at the quadrant, that is, the shape is (2k+ 1) 90 α, and the function name becomes redundant letters? Numbers, sine to cosine, cosine to sine, tangent to cotangent, cotangent to tangent. If the shape is 2k×90 α, the function name remains unchanged.