Tangent: Graph

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.

For y = a tan bx,
the period is π/|b|.

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.