# How do you determine the amplitude, period, and shifts to graph y=2cos2x?

Sep 30, 2016

amplitude = 2, period $= \pi$

#### Explanation:

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

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

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

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

here a = 2 , b = 2 , c = 0 and d = 0

amplitude = |2| = 2 and period $= \frac{2 \pi}{2} = \pi$