# What is the frequency of f(theta)= sin 7 t - cos 4 t ?

Jan 10, 2018

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

#### Explanation:

The period of the sum of $2$ periodic functions is the $\text{LCM}$ of their periods.

The period $\text{sin7t}$ is $= \frac{2 \pi}{7} = \frac{4 \pi}{14}$

The period $\text{cos4t}$ is $= \frac{2 \pi}{4} = \frac{7 \pi}{14}$

The $L C M$ of $\frac{2 \pi}{7}$ and $\frac{2 \pi}{4}$ is

$= \frac{28 \pi}{14} = 2 \pi$

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