Any sine function can be written as:
[tex]y = A sin(B(x + C)) + D[/tex]
Where:
[tex]amplitude \ is \ A \\ \\ period \ is \ 2\pi /B \\ \\ phase \ shift \ is \ C \\ \\ vertical \ shift \ is \ D[/tex]
So here we have:
[tex]y=-2sin(8x)-12[/tex]
By comparing, we can calculate the period as follows:
[tex]T:Period \\ \\ \\ T=\frac{2\pi}{B}=\frac{2\pi}{8} \\ \\ \therefore \boxed{T=\frac{\pi}{4}}[/tex]
