# What is the period of f(theta) = tan ( ( theta)/9)- sec ( ( 7theta)/ 6) ?

Feb 21, 2016

$\frac{108 \pi}{7}$

#### Explanation:

Period of tan x -->$\pi$
Period of $\tan \left(\frac{x}{9}\right) - \to 9 \pi$
Period of $\sec \left(\frac{7 x}{6}\right)$ = Period of $\cos \left(\frac{7 x}{6}\right)$
Period of $\cos \left(\frac{7 x}{6}\right) \to \frac{12 \pi}{7}$
Least multiple of $\left(9 \pi\right) \mathmr{and} \frac{12 \pi}{7}$ --> $9 \pi \left(\frac{12}{7}\right)$ --> $\frac{108 \pi}{7}$
Period of $f \left(x\right) - \to \frac{108 \pi}{7}$