# How do you find the amplitude and period for y=cos2x+1?

Dec 4, 2016

$\text{amplitude " =1" and period } = \pi$

#### Explanation:

The standard form of the $\textcolor{b l u e}{\text{cosine function}}$ is.

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

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

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

$\text{Here " a=1,b=2,c=0" and } d = 1$

$\Rightarrow \text{amplitude " =|1|=1" and period } = \frac{2 \pi}{2} = \pi$