# Tangent: Graph

How to graph the given tangent function: period of t = tan x and y = a tan bx, 1 example, and its solution.

## Graph: t = tan x

### Graph

This is the graph of y = tan x.

### Period

A cycle of a tangent is

the graph between the asymptotes.

For the middle cycle,

the asymptotes are x = ±π/2.

A period is the width of a cycle.

So the period of y = tan x is

π/2 - (-π/2) = π.

## Graph: y = a tan bx

### Formula

For y = a tan bx,

the period is π/|b|.

## Example

### Example

### Solution

See y = 4 tan 2x.

The number in the cosine is 2.

So the period is

π/|2|.

π/|2| = π/2

So π/2 is the period of y = 4 tan 2x.