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

Feb 3, 2015

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:

$\sin 2 \alpha = 2 \sin \alpha \cos \alpha$,

we have:

$y = 2 \cdot 2 \sin x \cos x = 2 \sin 2 x$.

So the amplitude is $2$.

This is the sinus function:

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

This is the $y = \sin 2 x$ function (the period becomes $\pi$):

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

and this is the $y = 2 \sin 2 x$ function:

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