# What is the frequency of f(theta)= sin 2 t - cos 8 t ?

Nov 30, 2017

The frequency is $= \left(\frac{1}{\pi}\right) H z$

#### Explanation:

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

The function is $f \left(\theta\right) = \sin \left(2 t\right) - \cos \left(8 t\right)$

The period of $\sin \left(2 t\right)$ is ${T}_{1} = \frac{2 \pi}{2} = \frac{8 \pi}{8}$

The period of $\cos \left(8 t\right)$ is ${T}_{2} = \frac{2 \pi}{8} = \frac{2 \pi}{8}$

The LCM of $\frac{8 \pi}{8}$ and $\left(2 \frac{\pi}{8}\right)$ is $T = \left(8 \frac{\pi}{8}\right) = \pi$

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

graph{sin(2x)-cos(8x) [-1.125, 6.67, -1.886, 2.01]}