# What is the period of f(theta)= sin 6 t - cos t ?

Aug 9, 2016

$2 \pi$

#### Explanation:

The period of both sin kt and cos kt = $2 \frac{\pi}{k}$.

Here, the period of the term sin 6t is $\frac{\pi}{3}$ and the period of - cos t

is $2 \pi$.

The larger $2 \pi$ is direcly 6 X the other period.

So, the period of the combined oscillation is $2 \pi$.

See how it works.

$f \left(t + p e r i o d\right) = f \left(t + 2 \pi\right)$

$= \sin \left(6 \left(t + 2 \pi\right)\right) - \cos \left(t + 2 \pi\right)$

$= \sin \left(6 t + 12 \pi\right) - \cos t$

$= \sin 6 t - \cos t$

$= f \left(t\right)$