Answer
$y=3\sin{(4x-8)}$.
Work Step by Step
The general form for the sinusoidal function is: $y=A\sin{(\omega x-\phi)}+B$ where $A$ is the amplitude, $B$ is the vertical shift, we need $\omega$ can be computed from the period by the formula $\omega=\frac{2\pi}{T}.$
The phase shift is $\frac{\phi}{\omega}$, hence $\phi=\omega\cdot\text{phase shift}.$
Hence here: $A=3$,
$B=0$,
$\omega=\frac{2\pi}{T}=\frac{2\pi}{\frac{\pi}{2}}=4$
$\phi=\omega\cdot\text{phase shift}=4\cdot2=8$.
Hence our function is: $y=3\sin{(4x-8)}$.
