# What is the period of f(t)=sin( t / 2 )+ cos( (t)/ 4) ?

$8 \pi$
Period of $\sin \left(\frac{t}{2}\right)$ --> $4 \pi$
Period of $\cos \left(\frac{t}{4}\right)$--> $8 \pi$
Least common multiple of $2 \pi$ and $8 \pi$ --> $8 \pi$
Period of f(t) --> $8 \pi$