# What is the period of f(t)=sin( (t)/4 )+ cos( (t)/5 ) ?

$40 \pi$
The period for sin kt and also cos kt is $2 \frac{\pi}{k}$.
Separately, the periods of $\sin \left(\frac{t}{4}\right) \mathmr{and} \cos \left(\frac{t}{5}\right)$ are $8 \pi \mathmr{and} 10 \pi$, respectively.
So, for the sum it is the least common multiple $40 \pi$.