# How do you find the amplitude, period, phase shift for y=1/2 cosx?

Sep 16, 2017

$\frac{1}{2} , 2 \pi , 0$

#### Explanation:

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

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

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

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

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

$\Rightarrow \text{amplitude "=|1/2|=1/2," period } = 2 \pi$

$\text{there is no phase shift}$