# How do you find the amplitude, period, phase shift given y=1+8cos(6x-pi)?

Nov 27, 2016

$8 , \frac{\pi}{3} , \frac{\pi}{6}$

#### Explanation:

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

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

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

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

Here a = 8 , b = 6 ,c$= - \pi$ and d = 1

Hence amplitude $= | 8 | = 8 , \text{period} = \frac{2 \pi}{6} = \frac{\pi}{3}$

$\text{phase shift} = - \frac{- \pi}{6} = \frac{\pi}{6}$

$\text{vertical shift} = 1 = \left(\begin{matrix}0 \\ 1\end{matrix}\right)$