# What is the period of f(t)=sin((4t)/3)+ cos( (t)/12 ) ?

$24 \pi$
Period of $\sin \left(\frac{4 t}{3}\right)$--> $\left(\frac{3}{4}\right) 2 \pi = \frac{6 \pi}{4} = \frac{3 \pi}{2}$
Period of $\cos \left(\frac{t}{12}\right)$ --> $\left(12\right) \left(2 \pi\right) = 24 \pi$
Find least common multiple of $\frac{3 \pi}{2} \mathmr{and} 24 \pi .$
It is $24 \pi$ because $\frac{3 \pi}{2} x \left(16\right) = 24 \pi$