# How do you determine the amplitude, period, and shifts to graph  y=2cosx?

Jul 12, 2017

$\text{see explanation}$

#### Explanation:

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

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

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

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

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

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

$\text{there are no shifts}$
graph{2cosx [-10, 10, -5, 5]}