# Graphing Tangent Function

The trigonometric ratios can also be considered as functions of a variable which is the measure of an angle. This angle measure can either be given in degrees or radians . Here, we will use radians.

Since , the tangent function is undefined when cos x = 0. Therefore, the tangent function has a vertical asymptote whenever cos x = 0.

Similarly, the tangent and sine functions each have zeros at integer multiples of because tan x = 0 when sin x = 0.

The graph of a tangent function y = tan x is looks like this:

### Properties of the Tangent Function, y = tan x.

Domain: , where n is an integer.

y -intercept: (0, 0)

x -intercept: , where n is an integer.

Period:

Symmetry: origin (odd function)

### Amplitude and Period of a Tangent Function

The tangent function does not have an amplitude because it has no maximum or minimum value.

The period of a tangent function, y = a tan bx , is the distance between any two consecutive vertical asymptotes.

Period =

Also see Trigonometric Functions.