# What is the period of f(t)=sin( t /44 )+ cos( (7t)/24 ) ?

Sep 18, 2016

$528 \pi$

#### Explanation:

Period of $\sin \left(\frac{t}{44}\right)$ --> $88 \pi$
Period of $\cos \left(\frac{7 t}{24}\right)$ --> $\frac{48 \pi}{7}$
Find least common multiple of $88 \pi$ and $\frac{48 \pi}{7}$

$88 \pi$ ... x (6) ... --> $528 \pi$
$\frac{48 \pi}{7}$ ... x (7)(11) ... --> $528 \pi$

Period of f(t) --> $528 \pi$