Question

What is the frequency of `f(theta)= sin 6 t - cos 2 t`?

Answer 1

It is `1/pi`.

Explanation:

We look for the period that is easier, then we know that the frequency is the inverse of the period.

We know that the period of both `sin(x)` and `cos(x)` is `2pi`. It means that the functions repeat the values after this period.

Then we can say that `sin(6t)` has the period `pi/3` because after `pi/3` the variable in the `sin` has the value `2pi` and then the function repeats itself.

With the same idea we find that `cos(2t)` has period `pi`.

The difference of the two repeats when both quantities repeat.
After `pi/3` the `sin` start to repeat, but not the `cos`. After `2pi/3` we are in the second cycle of the `sin` but we do not repeat yet the `cos`. When finally we arrive to `3/pi/3=pi` both `sin` and `cos` are repeating.

So the function has period `pi` and frequency `1/pi`.

graph{sin(6x)-cos(2x) [-0.582, 4.283, -1.951, 0.478]}