# How do you find the amplitude and period of y = cos 4x?

Aug 13, 2015

They can be determined by looking at the coefficients and their location.

#### Explanation:

Let's look at this equation:

$y = A \cos \left(B x\right)$

The $A$ and $B$ coefficients can tell us what the amplitude and period are.

First, $A$ tells us what the amplitude is. For example, the amplitude of $y = 2 \cos \left(x\right)$ would be simply $2$.

Second, $B$ tells us what the period is. In this case, we have to divide the normal period by $B$ in order to find the period.

For example, the period of cosine is $2 \pi$. Therefore, the period would be $\frac{2 \pi}{B}$

For your specific question, $y = \cos 4 x$, the amplitude would be $1$ and the period would be $\frac{2 \pi}{4}$, or $\frac{\pi}{2}$.

NOTE: I wanted to mention to be careful when finding the period of tangent, as the normal period of tangent is $\pi$. Therefore, to find the period, you would do $\frac{\pi}{B}$ instead.