# How do you find the amplitude and period of a function y=sin(3x)?

The amplitude measures the distance between the peaks of your function. Since the sine of a number is always bounded between $- 1$ and $1$, and the amplitude is actually half of that distance, the amplitude is $1$.
As for the period, you have that your variable is not $x$ but $3 x$. This means that, in a sense, the variable runs at three times the speed, and so it takes one third of the normal period, which means $\frac{2 \pi}{3}$.
$A \sin \left(\omega x + \phi\right)$ is $\frac{2 \pi}{\setminus} \omega$.