# What is the frequency of f(theta)= sin 3 t - cos 7 t ?

##### 1 Answer
Mar 17, 2016

$2 \pi$

#### Explanation:

Period of $\sin \left(3 t\right) - \to \left(2 \frac{\pi}{3}\right)$
Period of $\cos \left(7 t\right) - \to \left(2 \frac{\pi}{7}\right)$
Least multiple of $\left(2 \frac{\pi}{3}\right)$ and $\left(2 \frac{\pi}{7}\right)$ --> $\left(2 \pi\right)$

$\left(\frac{2 \pi}{3}\right)$ x 3 times = $2 \pi$
$\left(\frac{2 \pi}{7}\right)$ x 7 times = $2 \pi$

Period of $f \left(t\right) - \to 2 \pi$