I understand how to interpret the magnitude result from the FFT, but why is the phase that we obtain, arctan(Im(x)/Re(x)) indicative of the phase shift of a cosine graph, and not a sine graph?

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    $\begingroup$ I don't see how that's true – that gives you the phase of the complex sinusoid with frequency $x$, not of a cosine or sine. $\endgroup$ – Marcus Müller Jan 22 at 14:26

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