Question

What is the amplitude of `f(x)=4sin(x)cos(x)`?

Answer 1

The answer is: `2`.

The amplitude of a periodic function is the numer that multiply the function itself.
Using the double-angle formula of sinus, that says:

`sin2alpha=2sinalphacosalpha`,

we have:

`y=2*2sinxcosx=2sin2x`.

So the amplitude is `2`.

This is the sinus function:

graph{sinx [-10, 10, -5, 5]}

This is the `y=sin2x` function (the period becomes `pi`):

graph{sin(2x) [-10, 10, -5, 5]}

and this is the `y=2sin2x` function:

graph{2sin(2x) [-10, 10, -5, 5]}