Question

What is the amplitude of y = 4sin3x?

1/2
2
3
4

Answer 1

The most generic sine function you can write is

`y = A\sin(\omega x + \phi) + k`

Of all these constant,
`A` affects the amplitude,
`\omega` affects the wave length,
`\phi` and
`k` cause horizontal/vertical translation.

In your case,
`A = 4,\quad \omega = 3,\quad \phi = k = 0`

And we are interested in the amplitude, so we focus on
`A = 4`

The amplitude of the standard sine function is 1, so when you multiply by
`A`, the new amplitude is
`A` itself. In our case
`A = 4`, so the amplitude is 4.