# How do you find the period of sin(3x)?

$\sin 3 x = \sin \left(3 x + 2 \pi\right) = \sin \left[3 \left(x + \frac{2 \pi}{3}\right)\right] = \sin 3 x$
This means "after the arc rotating three time of $\left(x + \left(2 \frac{\pi}{3}\right)\right)$, sin 3x comes back to its initial value"
So, the period of sin 3x is $\frac{2 \pi}{3.}$