# What is the frequency of f(theta)= sin 12 t - cos 2 t ?

Feb 25, 2018

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

#### Explanation:

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

The period of $\sin 12 t$ is ${T}_{1} = \frac{2 \pi}{12}$

The period of $\cos \left(2 t\right)$ is ${T}_{2} = \frac{2 \pi}{2} = \frac{12 \pi}{12}$

The $\text{LCM}$ of ${T}_{1}$ and ${T}_{2}$ is $T = \frac{12 \pi}{12} = \pi$

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

graph{cos(12x)-sin(2x) [-1.443, 12.6, -3.03, 3.99]}