Calculating values of trig functions

[Felix83]

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?

 

[CrankFan]

http://math.exeter.edu/rparris/peanut/cordic.pdf

or try a web search for "CORDIC."

 

[Moo Of Doom]

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.

 

[HallsofIvy]

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.

 

[Moo Of Doom]

Really? Strange... I was just told that... oh well.