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> encountering Taylor and Maclaurin series in Calc I, and thinking “oh, that’s a cute trick.” ... somebody had actually put the stuff to good use

Aren't Taylor series expansions how calculators compute sine and cosine values?

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Not usually. https://en.wikipedia.org/wiki/CORDIC is a bit more common, or if they are using an approximation, some form of min-max rational function approximation.

Oh I mean you could close your eyes and throw a dart at the map of mathematics and find any clever application thanks to <<insert-name-here>>’s ingenuity. I’m just saying that I had, as of yet, not known about or encountered a significant use of Maclaurin series.

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