How does a calculator approximate a trig function. For example, you punch in sin(37deg) and the calculator will give you 0.6018150232. how does it figure this out?
Calculators use partial sums of power series to approximate sine and cosine. The power series for sine is: [tex]sin(x) = x - \frac{1}{3!} * x^{3} + \frac{1}{5!} * x^{5} - \frac{1}{7!} * x^{7} + ...[/tex] Cosine: [tex]cos(x) = 1 - \frac{1}{2!} * x^{2} + \frac{1}{4!} * x^{4} - \frac{1}{6!} * x^{6} + ...[/tex] I'm not sure how many terms they usually use, but that doesn't really matter. The more terms, the more accurate.
Moo Of Doom: I thought for a long time that calculators used power series but I've been told that is not true. Check out CranFan's suggestion about the CORDIC algorithm.