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

Aug 13, 2016

$18 \pi$

#### Explanation:

Period of tan t --> $\pi$
Period of $\cos \left(\frac{7 t}{9}\right)$ --> $9 \frac{2 \pi}{7} = 18 \frac{\pi}{7}$
Find least common multiple of $\pi \mathmr{and} \frac{18 \pi}{7}$

$\pi$ ...x (18) --> $18 \pi$
$\frac{18 \pi}{7}$ ...x (7) --> $18 \pi$
Period of f(t) --> $18 \pi$