What is the definition domain and value domain of tangent function?

The domain of y=tanx is {x|x≠kπ+π/2, k∈Z}

The range of values is: r

The minimum positive period is: T=π.

Parity: odd function.

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

Monotone reduced interval: none

Symmetry axis: none

Center of symmetry: (kπ/2,0 0) (k ∈ z)

Inverse function of function y=tanx.

Calculation method: Let two acute angles be A and B respectively, and give the following expression: If tanA= 1.9/5, then A = Arctan1.9/5; If tanB=5/ 1.9, then B=arctan5/ 1.9. If you want to find a specific angle, you can look it up or use a computer to calculate it.

Extended data:

The inverse function of the tangent function y=tanx in the open interval (x∈(-π/2, π/2)) is denoted as y=arctanx or y=tanx, which is called the arc tangent function. It represents the only fixed angle on (-π/2, π/2) whose tangent value is equal to x, that is, tan(arctan x)=x, and the domain of the arctangent function is r, that is, (-∞, +∞). The arctangent function is an inverse trigonometric function.

Because the tangent function y=tanx has no one-to-one correspondence in the domain R, there is no inverse function. Note that the monotone interval of the tangent function is selected here. Because the tangent function is monotonically continuous in the open interval (-π/2, π/2), the arc tangent function exists and is uniquely determined.

The arctangent function is obviously symmetrical with the function y=tanx and (x∈R) about the straight line y=x, and the asymptote is y=π/2 and y=-π/2.

Baidu Encyclopedia-Arctangent Function