Python: Calculate sine/cosine with a precision of up to 1 million digits

Question

Question is pretty self-explanatory. I\'ve seen a couple of examples for pi but not for trigo functions. Maybe one could use a Taylor series as done here but I\'m not entire

Answer 1

mpmath is the way:

from mpmath import mp
precision = 1000000
mp.dps = precision
mp.cos(0.1)

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If unable to install mpmath or any other module you could try polynomial approximation as suggested.

where Rn is the Lagrange Remainder

Note that Rn grows fast as soon as x moves away from the center x₀, so be careful using Maclaurin series (Taylor series centered in 0) when trying to calculate sin(x) or cos(x) of arbitrary x.