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.