# What is the period of f(t)=sin( t / 30 )+ cos( (t)/ 6 ) ?

The period of sin kt is $2 \frac{\pi}{k}$ and so is the period of cos kt..
Here, the period of $\sin \left(\frac{t}{30}\right) = 60 \pi$ and the period of $\cos \left(\frac{t}{6}\right) = 12 \pi$.
So,. the period of the sum is the least common multiple of the separate periods = $60 \pi$.