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

Dec 18, 2017

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

#### Explanation:

$\text{the equation of the sine in standard form is}$

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

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

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

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

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

$\text{phase shift } = - \frac{\frac{\pi}{4}}{1} = - \frac{\pi}{4}$

$\text{there is no vertical displacement}$