# How do you determine the amplitude for y= sin 4 x?

$y = 1 \cdot \sin \left(4 x\right)$ we do not write it but there is a $1$ there. That represents your AMPLITUDE !!!!
So this function is oscillating between $+ 1$ and $- 1$.
The $4$ in front of $x$ is used to find the Period of your function as:
$k = \frac{2 \pi}{p e r i o d}$ with $k = 4$ giving $p e r i o d = \frac{\pi}{2}$.