# What is the frequency of f(theta)= sin 4 t - cos 24 t ?

Aug 10, 2018

$\frac{2}{\pi}$

#### Explanation:

$f \left(t\right) = \sin 4 t - \cos 24 t$

The separate frequencies for the two terms are

${F}_{1} =$ reciprocal of the period $= \frac{4}{2 \pi} = \frac{2}{\pi}$ and

F_2 = 24/(2pi) = 12/pi.

The frequency F of $f \left(t\right)$ is given by

1/F = L/F_1 = M/F_2, for befitting integers L and M, givnig

Period $P = \frac{1}{F} = L \frac{\pi}{2} = M \frac{\pi}{12}$.

Note that 2 is a factor of 12.

Easily, the lowest choice is L = 1, M = 6 and

$P = \frac{1}{F} = \frac{\pi}{2}$ giving $F = \frac{2}{\pi}$.