I spent some time today thinking about how long it would take me to produce a table of sines and cosines by hand. Of course it depends on the density and the precision of the table, but my conclusion was that it wouldn't take excessively long. I'd start by calculating sin 1° using the Maclaurin series, then use angle addition formulas to work up to 2°, 4°, , etc, to 90°.

@mjd Surely that is a Taylor series since its not at x=0. Also seems to be the way most calculators and Maple do it (according to what I have read).

@mjd I reckon you could leverage special triangles to reduce your workload -- 15, 30 and 45º are all very straightforward, and would need only 1º to 7º to refine them. I think 18 and 36º are simple, too, so you could get multiples of 3º exactly. Everything is within 1º of those :o)

@mjd With a sufficiently small step size, you could even consider using the Taylor series approach with the usual ODE system defining sine and cosine; e.g.

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