# How do you find the amplitude, period, vertical and phase shift and graph y=sin(theta-pi/2)?

Mar 8, 2017

$1 , 2 \pi , 0 , \frac{\pi}{2}$

#### Explanation:

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

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

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

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

$\text{here } a = 1 , b = 1 , c = - \frac{\pi}{2} , d = 0$

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

$\text{phase shift "=-(-pi/2)/1=pi/2" there is no vertical shift}$