# What is the period of f(t)=sin( t / 36 )+ cos( (t)/7) ?

$504 \pi$
In $f \left(t\right)$ the period of $\sin \left(\frac{t}{36}\right)$ would be $\frac{2 \pi}{\frac{1}{36}} = 72 \pi$ .
Period of $\cos \left(\frac{t}{7}\right)$ would be $\frac{2 \pi}{\frac{1}{7}}$ =$14 \pi$.
Hence the period of $f \left(t\right)$ would be the least common multiple of $72 \pi$ and $14 \pi$ which is $504 \pi$