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.