# What is the amplitude, period and the phase shift of y= 5/2 cos (x/2) ?

Aug 30, 2016

amplitude $= \frac{5}{2}$
period $= 4 \pi$

#### Explanation:

The standard form of the 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 $= - \frac{c}{b} \text{ and vertical shift} = d$

here a $= \frac{5}{2}$ , b $= \frac{1}{2}$ , c = 0 and d = 0

Hence amplitude $= | \frac{5}{2} | = \frac{5}{2}$ and period $= \frac{2 \pi}{\frac{1}{2}} = 4 \pi$