Question

What is the frequency of `f(theta)= sin 7 t - cos 84 t`?

Answer 1

The frequency is `=7/(2pi)=1.114`

Explanation:

The period of the sum of 2 periodic functions is the LCM of their periods

`f(theta)=sin7t-cos84t`

The period of `sin7t` is `=2/7pi=12/42pi`

The period of `cos84t` is `=2/84pi=1/42pi`

The LCM of `12/42pi` and `1/42pi` is `12/42pi=2/7pi`

The frequency is

`f=1/T`

Frequency `f=1/(2/7pi)=7/(2pi)=1.114`