Question

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

Answer 1

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 `3x`. 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 `(2pi)/3`.
Otherwise, you can use the formula which states that the period of a function like
`Asin(omegax+phi)` is `(2pi)/\omega`.