Question

What is the frequency of `f(theta)= sin 6 t - cos 18 t`?

Answer 1

First find the period of each function ...

Explanation:

Period of `sin6t` is `(2pi)/6=(1/3)pi`

Period of `cos18t` is `(2pi)/18=(1/9)pi`

Next, find the smallest integer values for m and n, such that ...

`m(1/3)pi=n(1/9)pi` or `9m=3n`

This occurs when `n=3` and `m=1` , so the smallest combined period is `pi/3`

`pi/3~~1.047` radians

frequency = 1/period `=3/pi~~0.955`

hope that helped