Question

For y=-2sin(8x)-12, find the period:

Answer 1

Explanation:

Any sine function can be written as:

$y = A sin(B(x + C)) + D$

Where:

$amplitude \ is \ A \\ \\ period \ is \ 2\pi /B \\ \\ phase \ shift \ is \ C \\ \\ vertical \ shift \ is \ D$

So here we have:

$y=-2sin(8x)-12$

By comparing, we can calculate the period as follows:

$T:Period \\ \\ \\ T=\frac{2\pi}{B}=\frac{2\pi}{8} \\ \\ \therefore \boxed{T=\frac{\pi}{4}}$