# What is the period of the function y = cos 4x?

$\frac{\pi}{2}$
To find the period of the function,we can use the fact that the period is expressed as $\frac{2 \pi}{|} b |$, where $b$ is the coefficient on the $x$ term inside the function $\cos \left(x\right)$, namely $\cos \left(b x\right)$.
In this case, we have $y = a \cos \left(b x - c\right) + d$, where $a$, $c$ and $d$ are all $0$, so our equation becomes
$y = \cos \left(4 x\right) \to b = 4$, thus the period of the function is $\frac{2 \pi}{4} = \frac{\pi}{2}$