Question

What is the frequency of `f(theta)= sin 2 t - cos 8 t`?

Answer 1

The frequency is `=(1/pi) Hz`

Explanation:

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

The function is `f(theta)=sin(2t)-cos(8t)`

The period of `sin(2t)` is `T_1=(2pi)/2=(8pi)/(8)`

The period of `cos(8t)` is `T_2=(2pi)/8=(2pi)/(8)`

The LCM of `(8pi)/8` and `(2pi/8)` is `T=(8pi/8)=pi`

The frequency is `f=1/T=1/pi Hz`

graph{sin(2x)-cos(8x) [-1.125, 6.67, -1.886, 2.01]}