# What is the frequency of f(theta)= sin 3 t - cos 15 t ?

Aug 2, 2016

Period is $\frac{2 \pi}{3}$ and the frequency is its reciprocal, $\frac{3}{2 \pi}$.

#### Explanation:

Period of sin (3t) --> $\frac{2 \pi}{3}$
Period of cos (15t) -->$\frac{2 \pi}{15}$
Period of f(t) --> least common multiple of $\frac{2 \pi}{3}$ and $\frac{2 \pi}{15}$

$\frac{2 \pi}{3}$ ...x (1) --> $\frac{2 \pi}{3}$
$\frac{2 \pi}{15}$ ...x (5) --> $\left(2 \frac{\pi}{3}\right)$

Period of f(t) --> $\frac{2 \pi}{3}$.

The frequency = 1/(period)=$\frac{3}{2 \pi}$.