1. Let α be an arbitrary angle, and the values of the same trigonometric function with the same terminal angle are equal: tan(2kπ+α)=tanα.

2. Let α be an arbitrary angle, and the relationship between π+α and the trigonometric function value of α is tan(π+α)=tanα.

3. The relationship between arbitrary angle α and trigonometric function value of-α: tan (-α) =-tan α.

4. The relationship between π-α and the trigonometric function value of α can be obtained by Formula 2 and Formula 3: tan (π-α) =-tan α.

5. Using formula 1 and formula 3, we can get the relationship between the trigonometric function values of 2π-α and α: tan (2π-α) =-tan α.

Case study:

Properties of Tangent Function Images

Domain: {x | x≦(π/2)+kπ, k∈Z}

Scope: r

Parity: Yes, for odd function.

Periodic: Yes

Minimum positive period: kπ, k∈Z

Monotonicity: Yes.

Monotonic increasing interval: (-π/2+kπ, +π/2+kπ), k∈Z

Monotone reduced interval: none

Six basic functions

Function name: sine function cosine function tangent function cotangent function secant function cotangent function

Sinθ=y/r

Cosine function cosθ=x/r

Tangent function tanθ=y/x

Cotangent function cotθ=x/y

Secθ secθ=r/x

Cotangent function csθ= r/y