# What is the period of f(t)=sin( t / 36 )+ cos( (t)/9 ) ?

Apr 9, 2016

The period of the compounded oscillation $f \left(t\right) = \sin \left(\frac{t}{36}\right) + \cos \left(\frac{t}{9}\right)$ is 72pi#...

#### Explanation:

The period for both sin kt and cos kt is $2 \frac{\pi}{k}$.
The period of $\sin \left(\frac{t}{36}\right) = 72 \pi$.
The period of $\cos \left(\frac{t}{9}\right) = 18 \pi$.
18 is a factor of 72.

So, the period for the compounded oscillation is $72 \pi$.