# What is the amplitude, period, phase shift and vertical displacement of y=3sin(3x+pi)-1?

Feb 3, 2018

$3 , \frac{2 \pi}{3} , - \frac{\pi}{3} , - 1$

#### Explanation:

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

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

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

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

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

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

$\text{phase shift "=-pi/3" vertical shift } = - 1$