Question

What is the period of `f(theta) = tan ( ( 17 theta)/12 )- cos ( ( 3 theta)/ 4 )`?

Answer 1

`24pi`.

Explanation:

You need to find the smallest number of periods so that both functions have undergone an integer number of wavecycles.

`17/12 * n = k_0` and `3/4 * n = k_1` for some `n, k_0, k_1 in Z+`.

It is obvious by considering the denominators that `n` should be chosen to be `12`. Then each of the two functions have had a whole number of wave cycles every 12 wave cycles.

12 wave cycles at `2pi` per wave cycle gives a period of `24pi`.