# What is the frequency of f(theta)= sin 12 t - cos 16 t ?

Dec 29, 2016

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

#### Explanation:

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

The period of $\sin 12 t$ is $= \frac{2}{12} \pi = \frac{4}{24} \pi$

The period of $\cos 16 t$ is $= \frac{2}{16} \pi = \frac{3}{24} \pi$

$4 = 2 \cdot 2$

$3 = 3 \cdot 1$

LCM $\left(4 , 3\right) = 3 \cdot 2 \cdot 2 \cdot = 12$

The LCM of $\frac{\pi}{6}$ and $\frac{\pi}{8}$ is $= \frac{12}{24} \pi = \frac{\pi}{2}$

The period is $T = \frac{\pi}{2}$

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

$f = \frac{2}{\pi}$