# What is the phase shift, vertical displacement with respect to y=cosx for the graph y=cos(x-pi/3)?

Apr 14, 2017

$\text{ shift of " pi/3to" no vertical displacement}$

#### Explanation:

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

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

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

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

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

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

$\text{with respect to } y = \cos x$

$y = \cos \left(x - \frac{\pi}{3}\right) \text{ is " y=cosx" shifted " pi/3" to the right}$