I'm looking for a relatively simple algorithm that can quickly be done by hand to refine an initial estimate for the sine of an angle in degrees.
I've memorized a few landmark values for sine and come up with some simple techniques such that I can rapidly estimate the sine of any angle (in degrees) to within 10% error. What I'd like to do now is be able to take that estimate and refine it, presumably through some simple iterative algorithm that I can perform on a white board, for instance.