Finding the Amplitude and Period of a Sinusoidal Function

Determine the amplitude and period of \(y=-3\sin ( 4\pi x)\).

Solution Comparing \(y=-3\sin (4\pi x)\) to \(y = A\sin ( \omega x)\), we find that \(A = -3\) and \(\omega = 4\pi\). Then, \[ \hbox{Amplitude} =\vert A\vert =\vert {-}3\vert =3 \qquad \hbox{Period} =T=\dfrac{2\pi }{\omega }=\dfrac{2\pi }{4\pi }=\dfrac{1}{2} \]