# What is the frequency of f(theta)= sin 24 t - cos 14 t ?

Jul 24, 2017

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

#### Explanation:

We start by calculating the period.

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

The period of $\sin 24 t$ is ${T}_{1} = \frac{2}{24} \pi = \frac{1}{12} \pi = \frac{7}{84} \pi$

The period of $\cos 14 t$ is ${T}_{2} = \frac{2}{14} \pi = \frac{1}{7} \pi = \frac{12}{84} \pi$

The LCM of ${T}_{1}$ and ${T}_{2}$ is $T = \left(7 \cdot \frac{12}{84} \pi\right) = \frac{84}{84} \pi = \pi$

The frequency is $f = \frac{1}{T} = \frac{1}{\pi}$