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I'm trying to find a way to calculate the angular frequency of the following wave:

$$3\cos(2t)-2\sin(4t-1)$$

I know how to calculate the angular frequency for a cosine wave or sine wave by taking the coefficient of $t$, does it involve trigonometric identities? How do I go about getting the angular frequency of the sum of a cosine and a sine wave as above?

I plotted it on the graph and I could find it that way but would prefer to find it mathematically.

Any hints would be helpful.

Thanks

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    $\begingroup$ I would like to define angular frequency for a periodic function as $2\pi/T$ where $T$ is the period, but many sources (such as en.wikipedia.org/wiki/Angular_frequency) seem to define angular frequency only for pure sinusoidal functions. What definition are you using? $\endgroup$
    – David K
    Dec 10, 2022 at 17:41

2 Answers 2

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If frequencies are different there exists no common angular frequecy, it cannot be found.

If the frequencies are slightly different however we can have a $beat$ frequency.

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  • $\begingroup$ How about t and 2t? $\endgroup$
    – marty cohen
    Feb 27, 2018 at 20:27
  • $\begingroup$ They are different, no? $\endgroup$
    – Narasimham
    Feb 27, 2018 at 20:31
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$\begin{array}\\ 3\cos(2t)-2\sin(4t-1) &=3\cos(2t)-2(\sin(4t)\cos(1)-\cos(4t)\sin(1))\\ &=3\cos(2t)-2((2\sin(2t)\cos(2t)\cos(1)-(\cos^2(2t)-\sin^2(2t)\sin(1))\\ \end{array} $

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