# How do you find the period and amplitude of y=5/2cos(x/4)?

Mar 12, 2018

$\text{period "=8pi" and amplitude } = \frac{5}{2}$

#### Explanation:

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

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

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

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

$\text{here } a = \frac{5}{2} , b = \frac{1}{4} , c = d = 0$

$\text{amplitude "=|5/2|=5/2," period } = \frac{2 \pi}{\frac{1}{4}} = 8 \pi$