# What is the period of f(t)=sin( 4 t )+ cos( 24t ) ?

Feb 1, 2017

$\frac{\pi}{2}$.

#### Explanation:

The period of both $\sin k t \mathmr{and} \cos k t$ is $\frac{2 \pi}{k}$. So,

the period ${P}_{1}$of $\cos 24 t$ is$\frac{\pi}{12}$ and

the period ${P}_{2}$ of $\sin 4 t = \frac{\pi}{2} = 6 {P}_{1}$. And so,

the period of the compounded oscillation

$f \left(t\right) = \sin 4 t + \cos 24 t ,$

$P = {P}_{2} = \frac{\pi}{2} = 6 {P}_{1}$.