# What is the period of f(theta) = tan ( ( 5theta)/12 )- cos ( ( 5 theta)/ 3 ) ?

Feb 17, 2016

$\frac{12 \pi}{5}$

#### Explanation:

Period of tan x --> $\pi$
Period of $\tan \left(\frac{5 x}{12}\right)$ --> $\frac{12 \pi}{5}$
Period of cos x -->$2 \pi$
Period of cos ((5x)/3) --> $\frac{6 \pi}{5}$
Least multiple of $\frac{12 \pi}{5}$ and $\frac{6 \pi}{5}$ --> $\frac{12 \pi}{5}$
Period of f(x) -->$\frac{12 \pi}{5}$