We present a new table-based algorithm for the evaluation of the sine and cosine functions, which removes two sources of error in the final step of the evaluation. The tabulation of exact values for sines and cosines is realized thanks to a selection of "good" Pythagorean triples. A method for pre-computing such selections for tables indexed by up to 10 bits in reasonable time and memory consumption is shown, along with a theoretical efficiency comparison between our proposed scheme and the current state of the art of table-based algorithms.