# How do you find the amplitude, period, phase shift for y=cos(x-pi/6)?

Aug 4, 2017

$1 , 2 \pi , \frac{\pi}{6}$

#### Explanation:

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

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

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

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

$\text{here } a = 1 , b = 1 , c = - \frac{\pi}{6} , d = 0$

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

$\text{phase shift } = - \left(- \frac{\pi}{6}\right) = \frac{\pi}{6}$