# What is the period of f(theta) = tan ( ( 13 theta)/12 )- cos ( ( 3 theta)/ 4 ) ?

Jun 21, 2016

$24 \pi$

#### Explanation:

Period of $\tan \left(\frac{13 t}{12}\right)$ --> $\frac{12 \pi}{13}$
Period of $\cos \left(\frac{3 t}{4}\right)$ --> $\frac{8 \pi}{3}$
Period of f(t) --> least common multiple of $\frac{12 \pi}{13}$ and $\frac{8 \pi}{3}$

$\frac{12 \pi}{13}$ ...x ..(26) ...--> $24 \pi$
$\frac{8 \pi}{3}$ ...x...(9)....---> $24 \pi$
Period of f(t) --> $24 \pi$