Question

What is the frequency of `f(theta)= sin 2 t - cos 23 t`?

Answer 1

`1/(2pi)`.

Explanation:

The period of `sin 2t, P_1===(2pi)/2=pi` and

the period of `cos 23t, P_2=(2pi)/23.`

As `23P_2=2P_1=2pi`, the period P for the compounded oscillation

f(t) is the common value `2pi`, so that

`f(t+2pi).=sin(2t+4pi)- cos(23t+46pi)=sin 2t-cos 23t`

`= f(t)`. Checked that P is the least P, asf(t+P/2) is not f(t).

The frequency `= 1/P=1/(2pi)`