# How do you find the amplitude and period of f(x) = 3 cos (2/3)x?

Sep 16, 2017

$3 , 3 \pi$

#### Explanation:

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

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

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

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

$\text{here } a = 3 , b = \frac{2}{3} , c = d = 0$

$\Rightarrow \text{ amplitude "=|3|=3," period } = \frac{2 \pi}{\frac{2}{3}} = 3 \pi$