# How do you find the amplitude and period for the function y=5cos4theta?

May 6, 2018

#### Explanation:

The amplitude of $\cos x$ is $= 1$

Therefore,

the amplitude of $5 \cos \theta$ is $= 5$

For a periodic function

$f \left(x\right) = f \left(x + T\right)$

where $T$ is the period

Therefore,

$5 \cos 4 \theta = 5 \cos 4 \left(\theta + T\right)$

$= 5 \left(\cos \left(4 \theta + 4 T\right)\right)$

$= 5 \left(\cos 4 \theta \cos 4 T - \sin 4 \theta \sin 4 T\right)$

Comparing the $L H S$ and the $R H S$

$\left\{\begin{matrix}\cos 4 T = 1 \\ \sin 4 T = 0\end{matrix}\right.$

$\implies$, $4 T = 2 \pi$

$T = \frac{\pi}{2}$

The period is $= \frac{\pi}{2}$

graph{5cos(4x) [-12.66, 12.66, -6.33, 6.33]}