1, domain: {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 about a point (kπ/2+π/2,0) (k ∈ z).

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

Tangent law

In a plane triangle, the tangent theorem shows that the quotient obtained by dividing the sum of any two sides by the difference between the first side and the second side is equal to the quotient obtained by dividing the tangent of half the sum of the diagonals of these two sides by the tangent of the difference between the diagonals of the first side and the second side.

Franciscus Vieta (Fran &; CcedilOis Viète) once put forward the tangent theorem in his first book on trigonometry, Mathematical Rules Applied to Triangle, which is rarely mentioned in modern middle school textbooks. For example, because the Chinese criticized the former Soviet Union and its pedagogy, the tangent theorem was deleted from the middle school mathematics textbooks from 1966 to 1977, but when there was no computer-aided triangle solution,