# What is the period of f(theta) = tan ( ( 13 theta)/4 )- cos ( ( theta)/ 5 ) ?

Aug 16, 2016

$20 \pi$

#### Explanation:

Period of $\tan \left(\left(13 t\right) 4\right)$ --> $\frac{4 \pi}{13}$
Period of $\cos \left(\frac{t}{5}\right)$ --> $10 \pi$
Find least common multiple of $\frac{4 \pi}{13} \mathmr{and} 10 \pi$

$\frac{4 \pi}{13}$ ... x (5)(13) ... --> $20 \pi$
$10 \pi$ ... x (2) ... --> $20 \pi$