# What is the period of f(theta) = tan ( ( 17 theta)/7 )- cos ( ( theta)/ 6 ) ?

May 30, 2018

$84 \pi$

#### Explanation:

Period of $\tan \left(\frac{17 \pi}{7}\right)$ --> $\frac{7 \left(\pi\right)}{17}$
Period of $\cos \left(\frac{t}{6}\right)$ ---> $6 \left(2 \pi\right) = 12 \pi$
Period of f(t) is least common multiple of $12 \pi \mathmr{and} \frac{7 \pi}{17}$.

$\frac{7 \pi}{17}$ ..... x (17)(12) ... --> $84 \pi$
$12 \pi$...............x (5) ....... --> $84 \pi$

Period of f(t) is $84 \pi$