# How do you find the period and amplitude of y=5/2cos(x/2)?

Oct 21, 2017

Amplitude = 5/2, Period $= \ast 4 \pi \ast$

#### Explanation:

Use the form $a \cdot \cos \left(b x - c\right) + d$

Given equation is $y = \left(\frac{5}{2}\right) \cos \left(\frac{x}{2}\right)$

In this equation
$a = \frac{5}{2} , b = \frac{1}{2} , c = 0 , d = 0$

Amplitude = $a = \frac{5}{2}$

Period $= \frac{2 \pi}{b} = \frac{2 \pi}{\frac{1}{2}} = 4 \pi$

Phase shift = c/b = 9

Vertical shift = d = 0
graph{(5/2) cos (x/2) [-10, 10, -5, 5]}