# What is the period of the graph of the equation y= 3 cos 4x?

Jun 30, 2016

the period of the given fun. is $\frac{\pi}{2.}$

#### Explanation:

We know that the Principal Period of cosine fun. is $2 \pi .$ This means that, $\forall \theta \in \mathbb{R} , \cos \left(\theta + 2 \pi\right) = \cos \theta \ldots \ldots . \left(1\right)$

Let $y = f \left(x\right) = 3 \cos 4 x$

But, by $\left(1\right) , \cos 4 x = \cos \left(4 x + 2 \pi\right)$

$\therefore f \left(x\right) = 3 \cos 4 x = 3 \cos \left(4 x + 2 \pi\right) = 3 \cos \left\{4 \left(x + \frac{\pi}{2}\right)\right\} = f \left(x + \frac{\pi}{2}\right) ,$ i.e., $f \left(x\right) = f \left(x + \frac{\pi}{2}\right)$.

This shows that the period of the given fun.$f$ is $\frac{\pi}{2.}$