Let us suppose the sine function is in the form
[tex]y=A\sin(Bx)+D[/tex]
We have been given that the amplitude is 4. It means we have
[tex]A=4[/tex]
Now, period is given by [tex]\frac{\pi}{6}[/tex]
Thus, we have
[tex]\frac{2\pi}{B} =\frac{\pi}{6} \\ \\ B=12[/tex]
Now, we have been given that the mid line is[tex]y=-2[/tex]. Hence, we have
[tex]D=-2[/tex]
Therefore, the sine function is given by
[tex]y=4\sin(12x)-2[/tex]
