Tan is a tangent. Take a right triangle with hypotenuse length c, side length a and adjacent side length b as an example. In the mathematical function, tan represents the tangent value, so tan∠ 1=a:b (that is, the opposite side of tan ∠ 1: adjacent side) can be found by Tan when two right-angled sides are known. Tan is a tangent function, which is the ratio of the opposite side to the adjacent side in a right triangle.

The property of the tangent function is 1, and the domain is {x | x≦(π/2)+kπ, k∈Z}.

2. scope: real number set R.

3. Parity: odd function.

4. Monotonicity: increasing function in the interval (-π/2+kπ, π/2+kπ) and (k∈Z).

5. Periodicity: The minimum positive period π (can be obtained by T=π/|ω|).

6. Maximum value: there is no maximum value and minimum value.

7. Zero point: kπ, k ∈ z.

8. Symmetry: Axisymmetric: Axisymmetric: Symmetry (k∈Z) about the point (k π/2+π/2,0).

9. Parity: From tan(-x)=-tan(x), we know that the tangent function is odd function, and its image is centrosymmetric about the origin.

10, all x=(n/2)π(n∈Z) of the tangent curve are its symmetry centers except the origin.

Trigonometric function knowledge point Trigonometric function is one of the basic elementary functions, with angle as the independent variable, and the coordinate or its ratio corresponding to the intersection of the terminal edge of any angle and the unit circle as the dependent variable. When you come into contact with trigonometric function in junior high school, you should understand that it is the basis of trigonometric function in senior high school, and it is also the key and difficult point and necessary test point of senior high school mathematics. Trigonometric function is a kind of transcendental function and belongs to elementary function.

See the problem of "finding the angle", and use the "emerging" inductive formula to transform it into the interval formula in one step: (-90o, 90o). sin(kπ+α)=(- 1)ksinα(k∈z)； cos(kπ+α)=(- 1)kcosα(k∈Z)； tan(kπ+α)=(- 1)ktanα(k∈Z)； cot(kπ+α)=(- 1)kcotα(k∈Z).