What is the frequency of f(theta)= sin 12 t - cos 84 t ?

Mar 4, 2017

The frequency is $= 1.91$

Explanation:

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

The period of $\sin 12 t$ is $= \frac{2 \pi}{12} = \frac{\pi}{6}$

The period of $\cos 84 t$ is $= \frac{2 \pi}{84} = \frac{\pi}{42}$

The LCM of $\frac{\pi}{6}$ and $\frac{\pi}{42}$ is $= \frac{7 \pi}{42} = \frac{\pi}{6}$

The frequency is

$f = \frac{1}{T} = \frac{1}{\frac{\pi}{6}} = \frac{6}{\pi} = 1.91$