# How do you find the period for y=20cos((2/3)x+pi)+2?

May 30, 2018

$\text{period } = 3 \pi$

#### Explanation:

$\text{the standard form of the cosine function is}$

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{y = a \cos \left(b x + c\right) + d} \textcolor{w h i t e}{\frac{2}{2}} |}}}$

$\text{where amplitude "=|a|," period } = \frac{2 \pi}{b}$

$\text{phase shift "=-c/b" and vertical shift } = d$

$\text{here "b=2/3rArr"period } = \frac{2 \pi}{\frac{2}{3}} = 3 \pi$