Question

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

Answer 1

The period is `=24/5pi`

Explanation:

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

The period of `tan(5/12theta)` is

`T_1=(pi)/(5/12)=12/5pi`

The period of `cos(5/4theta)` is

`T_2=(2pi)/(5/4)=8/5pi`

The LCM of `12/5pi` and `8/5pi` is

`T=24/5pi`

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