# How do you determine the amplitude, period and vertical translation of y=3sin4x-5?

May 31, 2018

$3 , \frac{\pi}{2} , - 5$

#### Explanation:

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

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

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

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

$\text{here } a = 3 , b = 4 , c = 0 , d = - 5$

$\text{amplitude "=|3|=3," period } = \frac{2 \pi}{4} = \frac{\pi}{2}$

$\text{vertical shift } = - 5$