Question

What is the period of `f(theta) = tan ( ( 13 theta)/4 )- cos ( ( 6 theta)/ 5 )`?

Answer 1

`(20pi)/39`

Explanation:

`tanx` has a period of `pi`, while `cos x` has a period of `2pi`

Thus `tan((13theta)/4)` completes one period, when `theta` changes by `(4pi)/13`, while

`cos((6pi)/5)` repeats when `theta` changes by `(5pi)/3`

So, the period of `f(theta)` is the least common multiple of `(4pi)/13` and `(5pi)/3`, i.e. `(20pi)/39`