# What is the amplitude, period, phase shift and vertical displacement of y=sin(x-pi/4)?

Jul 26, 2017

$1 , 2 \pi , \frac{\pi}{4} , 0$

#### Explanation:

$\text{the standard form of the "color(blue)"sine function }$ is.

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

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

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

$\text{here } a = 1 , b = 1 , c = - \frac{\pi}{4} , d = 0$

$\Rightarrow \text{ amplitude "=1,"period } = 2 \pi$

$\text{phase shift } = - \left(- \frac{\pi}{4}\right) = \frac{\pi}{4}$

$\text{there is no vertical shift}$