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

Jul 23, 2017

$24 \pi$.

#### Explanation:

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

$\frac{17}{12} \cdot n = {k}_{0}$ and $\frac{3}{4} \cdot n = {k}_{1}$ 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 $2 \pi$ per wave cycle gives a period of $24 \pi$.