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

Feb 18, 2017

$\frac{1}{2 \pi}$.

#### Explanation:

The period of $\sin 2 t , {P}_{1} = = = \frac{2 \pi}{2} = \pi$ and

the period of $\cos 23 t , {P}_{2} = \frac{2 \pi}{23.}$

As $23 {P}_{2} = 2 {P}_{1} = 2 \pi$, the period P for the compounded oscillation

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

$f \left(t + 2 \pi\right) . = \sin \left(2 t + 4 \pi\right) - \cos \left(23 t + 46 \pi\right) = \sin 2 t - \cos 23 t$

$= f \left(t\right)$. Checked that P is the least P, asf(t+P/2) is not f(t).

The frequency $= \frac{1}{P} = \frac{1}{2 \pi}$