# What is the period of f(theta) = tan ( ( 7 theta)/12 )- cos ( ( 3 theta)/ 4 ) ?

Sep 14, 2016

$24 \pi$

#### Explanation:

Period of $\tan \left(\frac{7 \pi}{12}\right)$ --> $\frac{12 \pi}{7}$
Period of $\cos \left(\frac{3 t}{4}\right)$ --> $\frac{8 \pi}{3}$
Find least common multiple of $\frac{12 \pi}{7}$ and $\frac{8 \pi}{3}$
$\frac{12 \pi}{7}$ ... x (7)(2) ...--> $24 \pi$
$\frac{8 \pi}{3}$ ... x (3)(3) ... --> $24 \pi$
Period of f(t) --> $24 \pi$