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

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

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Answer 1 · 2016-04-18T08:14:26

$\frac{3}{2 π}$ $3/(2pi)$

Explanation:

Noting that $sin (t)$ $sin(t)$ and $cos (t)$ $cos(t)$ both have a period of $2 π$ $2pi$ , we can say that the period of $sin (3 t) - cos (21 t)$ $sin(3t)-cos(21t)$ will be $\frac{2 π}{gcd (3, 21)} = \frac{2 π}{3}$ $(2pi)/("gcd"(3,21))=(2pi)/3$ , 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 $P$ $P$ and frequency $f$ $f$ , we have $f = \frac{1}{P}$ $f = 1/P$ .

In this case, as we have the period as $\frac{2 π}{3}$ $(2pi)/3$ , that gives us a frequency of $\frac{3}{2 π}$ $3/(2pi)$

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

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