# What is the period of f(theta) = tan ( ( 5theta)/12 )- cos ( ( 5 theta)/ 4 ) ?

May 13, 2018

The period is $= \frac{24}{5} \pi$

#### Explanation:

The period of the sum of $2$ periodic functions is the LCM of their periods.

The period of $\tan \left(\frac{5}{12} \theta\right)$ is

${T}_{1} = \frac{\pi}{\frac{5}{12}} = \frac{12}{5} \pi$

The period of $\cos \left(\frac{5}{4} \theta\right)$ is

${T}_{2} = \frac{2 \pi}{\frac{5}{4}} = \frac{8}{5} \pi$

The LCM of $\frac{12}{5} \pi$ and $\frac{8}{5} \pi$ is

$T = \frac{24}{5} \pi$

graph{tan(5/12x)-cos(5/4x) [-20.27, 20.29, -10.14, 10.13]}