# What is the period of f(theta)= sin 7 t - cos 5 t ?

Mar 18, 2016

$2 \pi$

#### Explanation:

Period of sin (7t) --> $\left(2 \frac{\pi}{7}\right)$
Period of cos (5t) --> $\left(2 \frac{\pi}{5}\right)$
Least common multiple of $\frac{2 \pi}{7}$ and $\frac{2 \pi}{5}$ --> $2 \pi$

$\left(\frac{2 \pi}{7}\right)$ x (7) --> $2 \pi$
$\left(\frac{2 \pi}{5}\right)$ x (5) --> $2 \pi$

Answer: Period of f(t) --> $2 \pi$