# How do you find the period of y = 2 tan 3x?

$\frac{\pi}{3}$
The period of the tangent function is $\pi$. Therefore, the period of $\tan \left(3 x\right)$ is $\frac{\pi}{3}$ ($3 x$ will increase by $\pi$ units anytime $x$ increases by $\frac{\pi}{3}$ units). This means the period of $y = 2 \tan \left(3 x\right)$ is $\frac{\pi}{3}$ as well. The "2" is irrelevant.