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

1 Answer
Luke Phillips
Jul 23, 2017

#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#.

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