## Calculating values of trig functions

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?

 Read this or try a web search for "CORDIC."
 Calculators use partial sums of power series to approximate sine and cosine. The power series for sine is: $$sin(x) = x - \frac{1}{3!} * x^{3} + \frac{1}{5!} * x^{5} - \frac{1}{7!} * x^{7} + ...$$ Cosine: $$cos(x) = 1 - \frac{1}{2!} * x^{2} + \frac{1}{4!} * x^{4} - \frac{1}{6!} * x^{6} + ...$$ I'm not sure how many terms they usually use, but that doesn't really matter. The more terms, the more accurate.

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