# What is the period of f(t)=sin(t/2)+ sin( (2t)/5) ?

$20 \pi$
Period of sin t --> $2 \pi$
Period of $\sin \left(\frac{t}{2}\right)$ --> $4 \pi$
Period of $\sin \left(\frac{2 t}{5}\right)$ --> $\frac{10 \pi}{2} = 5 \pi$
Common period of f(t) --> $20 \pi$