# How do you find the amplitude and period for y=3cosx+2?

Dec 8, 2016

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

#### Explanation:

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

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

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

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

Here a = 3 , b = 1 , c = 0 and d =2

$\Rightarrow \text{amplitude " =|3|=3 , "period } = \frac{2 \pi}{1} = 2 \pi$