Question

What is the frequency of `f(theta)= sin 3 t - cos 21 t`?

Answer 1

`3/(2pi)`

Explanation:

Noting that `sin(t)` and `cos(t)` both have a period of `2pi`, we can say that the period of `sin(3t)-cos(21t)` will be `(2pi)/("gcd"(3,21))=(2pi)/3`, which is the least positive value such that both terms will finish a period simultaneously.

We know that the frequency is the inverse of the period, that is, given period `P` and frequency `f`, we have `f = 1/P`.

In this case, as we have the period as `(2pi)/3`, that gives us a frequency of `3/(2pi)`