# How do you find the amplitude, period, phase shift for y=sin(x-pi/4)?

Nov 27, 2016

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

#### Explanation:

The standard form of the $\textcolor{b l u e}{\text{sine function}}$ is.

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

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

phase shift $= - \frac{c}{b}$ and vertical shift = d

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

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

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