Question

How do you determine the amplitude and period of `y=3sin4x`?

Answer 1

You can "read" these information from the numbers in your function, i.e, `3` (multiplying `sin`) and `4` (multiplying `x`):
Amplitude is `3` meaning that your function oscillates between `+3 and -3`;
Period is given using `4` in the form of: `(period)=(2pi)/color(red)(4)=pi/2`