# What is the frequency of f(theta)= sin 18 t - cos 81 t ?

Feb 22, 2017

The frequency is $= \frac{9}{2 \pi}$

#### Explanation:

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

The period of $\sin 18 t$ is $= \frac{2}{18} \pi = \frac{1}{9} \pi = \frac{9}{81} \pi$

The period of $\sin 81 t$ is $= \frac{2}{81} \pi$

The LCM of $\frac{9}{81} \pi$ and $\frac{2}{81} \pi$ is $= \frac{18}{81} \pi = \frac{2}{9} \pi$

The period is $T = \frac{2}{9} \pi$

The frequency is $f = \frac{1}{T} = \frac{9}{2 \pi}$