# What is the frequency of f(theta)= sin 24 t - cos 7 t ?

Jul 10, 2017

The frequency is $= \frac{1}{2 \pi}$

#### Explanation:

The period of the sum of $2$ periodic functions is the LCM of their periods

The period of $\sin 24 t$ is ${T}_{1} = \frac{2 \pi}{24}$

The period of $\cos 7 t$ is ${T}_{2} = \frac{2 \pi}{7}$

The LCM of ${T}_{1}$ and ${T}_{2}$ is $T = \frac{168 \pi}{84} = 2 \pi$

The frequency is

$f = \frac{1}{T} = \frac{1}{2 \pi}$