# What is the frequency of f(t)= sin 12 t - cos 54 t ?

Jan 10, 2017

Find the overall period by finding least common multiple of the two periods. The overall frequency is the reciprocal of the overall period.

#### Explanation:

Let ${\tau}_{1} =$ the period of the sine function $= \frac{2 \pi}{12}$
Let ${\tau}_{2} =$ the period of the cosine function $= \frac{2 \pi}{54}$

${\tau}_{\text{overall}} = L C M \left(\frac{2 \pi}{12} , \frac{2 \pi}{54}\right) = \frac{\pi}{3}$

${f}_{\text{overall") =1/tau_("overall}} = \frac{3}{\pi}$