# What is the amplitude, period and the phase shift of  y=tan 2x?

Jun 20, 2018

#### Explanation:

The amplitude of $\tan 2 x$ is $\mathbb{R}$

The period of a periodic function $f \left(x\right)$ is such that

$f \left(x\right) = f \left(x + T\right)$

Here,

$f \left(x\right) = \tan 2 x$

Therefore,

$\tan 2 x = \tan 2 \left(x + T\right) = \tan \left(2 x + 2 T\right)$

$= \frac{\tan 2 x + \tan 2 T}{1 - \tan 2 x \tan 2 T}$

So,

$\tan \left(2 T\right) = 0$

$\implies$, $2 T = \pi$

$\implies$, $T = \frac{\pi}{2}$

The period is $T = \frac{\pi}{2}$

There is no phase shift.

graph{tan(2x) [-7.9, 7.9, -3.95, 3.95]}