Answer
$y=2 \ \sin (2x+4)$
Work Step by Step
The general form for the sinusoidal function can be expressed as:
$y=A\sin{(\omega x-\phi)}+B ..(1)$
where $A$ is the amplitude and $B$ represents the vertical shift.
The $\omega$ can be found from the period by the formula:
$\omega=\dfrac{2\pi}{T}$
and the phase shift is $\dfrac{\phi}{\omega}$.
This means that $\phi=\omega \times \ Phase \ Shift$
We have: $A=2$, $B=0$,
$\omega=\dfrac{2\pi}{T}=\dfrac{2\pi}{ \pi}=2$
$\phi=(2)(-2)=-4$
Therefore, our sinusoidal function (1) becomes: $y=2 \ \sin (2x+4)$