# How do you find the amplitude and period of y=2 cos(x+(pi/3))?

Apr 26, 2018

$2 , 2 \pi$

#### Explanation:

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

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

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

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

$\text{here "a=2,b=1,c=pi/3" and } d = 0$

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