# How do you find the amplitude, period, phase shift for y=cos(x+pi/2)?

Dec 23, 2016

$\text{amplitude " =1," period" =2pi," phase shift} = - \frac{\pi}{2}$

#### Explanation:

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

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

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

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

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

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

$\text{and phase shift } = - \frac{\frac{\pi}{2}}{1} = - \frac{\pi}{2}$