# Tangent: Graph

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

## y = tan xPeriod

This is the graph of y = tan x.

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.

## y = a tan bxPeriod

For y = a tan bx,

the period is π/|b|.

## Exampley = 4 tan 2x, Period = ?

Solution

Solution (Detail)

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.