Question

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

Answer 1

Every time you have a trigonometric function have a look at the number that is multiplying it, basically the number "in front" of it:
In this case you have:
`y=1*sin(4x)` 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=(2pi)/(period)` with `k=4` giving `period=pi/2`.