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

Mar 14, 2017

The period is $= 2 \pi$

#### Explanation:

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

Period of $\sin 5 t$ is $= \frac{2}{5} \pi$

Period of $\cos t$ is $= 2 \pi$

The LCM of $\frac{2}{5} \pi$ and $2 \pi$ is $= \frac{10}{5} \pi = 2 \pi$

Therefore,

$T = 2 \pi$