# How do you find the amplitude, period, and shift for y=2sin(x-45°)-1?

May 19, 2018

$2 , {360}^{\circ} , {45}^{\circ} , - 1$

#### Explanation:

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

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

$\text{where amplitude "=|a|," period } = \frac{{360}^{\circ}}{b}$

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

$\text{here "a=2,b=1,c=-45^@" and } d = - 1$

$\text{amplitude "=|2|=2," period } = {360}^{\circ} / 1 = {360}^{\circ}$

$\text{phase shift "=-(-45^@)/1=45^@,"vertical shift } = - 1$