# How do you find the amplitude, period, and shift for y = 3 sin(3x- π)?

Aug 5, 2018

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

#### Explanation:

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

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

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

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

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

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

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