# What is the period of cos nx?

Mar 10, 2018

the period of the function
$\cos n x$
is
$x = \frac{2 \pi}{n}$

#### Explanation:

$\cos n x$
$n = 1$
$\cos n x = \cos 1 x$
$\cos x$
has period of $x = 2 \pi$
$x = \frac{2 \pi}{1}$
$n = 2$
$\cos n x = \cos 2 x$
$\cos 2 x$
has period of $2 x = 2 \pi$
$x = \frac{2 \pi}{2}$
$n = 3$
$\cos n x = \cos 3 x$
$\cos 3 x$
has period of $3 x = 2 \pi$
$x = \frac{2 \pi}{3}$

Hence, the period of the function
$\cos n x$
is
$x = \frac{2 \pi}{n}$