# How do you identify the amplitude, period and phase shift given the function y=3sin(2x-pi/2)?

Apr 21, 2018

$3 , \pi , \frac{\pi}{4}$

#### Explanation:

$\text{the standard form of the sine function is}$

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

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

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

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

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

$\text{phase shift } = - \frac{- \frac{\pi}{2}}{2} = \frac{\pi}{4}$