How does a calculator determine sin(12) or e raised to the square root of 2 or log(123456)?

Answer

Dear John,

It uses approximations based on sets of easily computable polynomials such as Chebyshev polynomials. One can of course use series developments, but they converge much more slowly, such as e^x=1+x+x^2/2!+x^3/3!+x^4/4!+….. and do not become more used. If speed is important, one can even calculate a function such as a sine in advance and put it into memory (and possibly interpolate to limit the memory required).

Hopefully this lifts the tip of the veil,
Manu Van Lili