# What is the frequency of f(t)= sin 3 t - cos 27 t ?

Aug 30, 2016

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

#### Explanation:

Frequency is the reciprocal of the period.

The period of both sin kt and cos kt is $\frac{2}{k} \pi$. So,

the separate periods for

$\sin 3 t \mathmr{and} \cos 27 t$

are

$\frac{2}{3} \pi \mathmr{and} \frac{2}{27} \pi$. The period P for

$f \left(t\right) = \sin 3 t - \cos 27 t$ is given by

$P = M \left(\frac{2}{3} \pi\right) = N \left(\frac{2}{27}\right) \pi$, where M and N are positive giving P

as the least positive-even-integer-multiple of $\pi$.

Easily, M = 3 and N = 27, giving $P = 2 \pi$.

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