# What is the frequency of f(theta)= sin 6 t - cos 45 t ?

May 31, 2017

The frequency is $= \frac{3}{2 \pi}$

#### Explanation:

We start by calculating the period of

$f \left(t\right) = \sin 6 t - \cos 45 t$

The period of the sum (or difference) of $2$ periodic functions is the LCM of their periods

The period of $\sin 6 t$ is $= \frac{2}{6} \pi = \frac{1}{3} \pi$

The period of $\cos 45 t$ is $= \frac{2}{45} \pi$

The LCM of $\frac{1}{3} \pi$ and $\frac{2}{45} \pi$ is

$= \frac{30}{45} \pi = \frac{2}{3} \pi$

So,

$T = \frac{2}{3} \pi$

The frequency is

$f = \frac{1}{T} = \frac{3}{2 \pi}$