# How do you find the period of y=3sin(x-2pi/3)-2?

Jul 9, 2018

the searched period is $2 \pi$

#### Explanation:

Calculating
$\sin \left(x - 2 \frac{\pi}{3} + 2 \pi\right) =$
$\sin \left(x - 2 \frac{\pi}{3}\right) \cos \left(2 \pi\right) + \cos \left(x - \frac{2}{3} \cdot \pi\right) \cdot \sin \left(2 \pi\right)$
since $\sin \left(2 \pi\right) = 0$ and $\cos \left(2 \pi\right) = 1$
we get

$\sin \left(x - \frac{2}{3} \cdot \pi + 2 \pi\right) = \sin \left(x - \frac{2}{3} \cdot \pi\right)$