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.