# What is the frequency of f(theta)= sin 3 t - cos 21 t ?

$\frac{3}{2 \pi}$
Noting that $\sin \left(t\right)$ and $\cos \left(t\right)$ both have a period of $2 \pi$, we can say that the period of $\sin \left(3 t\right) - \cos \left(21 t\right)$ will be $\frac{2 \pi}{\text{gcd} \left(3 , 21\right)} = \frac{2 \pi}{3}$, which is the least positive value such that both terms will finish a period simultaneously.
We know that the frequency is the inverse of the period, that is, given period $P$ and frequency $f$, we have $f = \frac{1}{P}$.
In this case, as we have the period as $\frac{2 \pi}{3}$, that gives us a frequency of $\frac{3}{2 \pi}$