# How do you find the amplitude, period and phase shift for y=3cos(theta-pi/3)?

Jan 17, 2017

$3 , 2 \pi , \frac{\pi}{3}$

#### Explanation:

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

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

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

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

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

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

$\text{and phase shift } = - \frac{- \frac{\pi}{3}}{1} = \frac{\pi}{3}$