What is the frequency of f(theta)= sin 3 t - cos 14 t ?

Jan 15, 2017

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

Explanation:

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

Period of $\sin 3 t$ is $= \frac{2 \pi}{3} = \frac{14 \pi}{21}$

Period of $\cos 14 t$ is $= \frac{2 \pi}{14} = \frac{\pi}{7} = \frac{3 \pi}{21}$

The LCM of $\frac{14 \pi}{21}$ and $\frac{3 \pi}{21}$ is $= \frac{42 \pi}{21} = 2 \pi$

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