# What is the period of f(t)=sin( t / 30 )+ cos( (t)/ 9 ) ?

Jul 1, 2016

$180 \pi$

#### Explanation:

Period of $\sin \left(\frac{t}{30}\right)$ --> $60 \pi$
Period of $\cos \left(\frac{t}{9}\right)$ --> $18 \pi$
Period of f(t) --> least common multiple of $60 \pi$ and $18 \pi$
$60 \pi$ ...x (3) --> $180 \pi$
$18 \pi$...x (10) --> $180 \pi$
Period of f(t) --> $180 \pi$