# How do you find the amplitude and period of y=4cos(72pit)?

May 30, 2017

$A m p l i t u \mathrm{de} = 4$
$P e r i o d = \frac{1}{36}$

#### Explanation:

For a cos (or sin) function of the form

$y = a \cos \left(b t\right) + c$

the period is given by

$P e r i o d = \frac{2 \pi}{b}$

and the amplitude is given by a

$A m p l i t u \mathrm{de} = a$

In this case

$a = 4$
$b = 72 \pi$

Therefore

$P e r i o d = \frac{2 \pi}{72 \pi} = \frac{1}{36}$

$A m p l i t u \mathrm{de} = 4$