# What is the frequency of f(theta)= sin 4 t - cos 13 t ?

Jan 6, 2017

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

#### Explanation:

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

The period of $\sin 4 t$ is $= \frac{2 \pi}{4} = \frac{\pi}{2} = \frac{13 \pi}{26}$

The period of $\cos 13 t$ is $= \frac{2 \pi}{13} = \frac{4 \pi}{26}$

The LCM of $\frac{13 \pi}{26}$ and $\frac{4 \pi}{26}$ is $= \frac{52 \pi}{26} = 2 \pi$

The period is $T = 2 \pi$

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