# What is the period and amplitude for y=2tan(3x-pi2)?

Jun 19, 2015

Amplitude= $\infty$
Period= $\frac{{\pi}^{2} + \pi}{3}$

#### Explanation:

The amplitude is infinity. Because the $\tan$ function is increasing over its whole domain of definition.
graph{tanx [-10, 10, -5, 5]}

The period of any $\tan$ is the value of $x$ when the "inside" of the $\tan \textcolor{red}{}$ function equals $\pi$.

I'll assume that,
$y = 2 \tan \left(3 x - {\pi}^{2}\right)$

For a period $3 x - {\pi}^{2} = \pi$

$\implies x = \frac{{\pi}^{2} + \pi}{3}$