1. A method for generating a sine and cosine of an input angle, comprising the steps of: decomposing said input angle into an octant or quadrant, a coarse angle, and a fine angle; determining a cosine and a sine of said coarse angle; decomposing said cosine of said coarse angle to a first most significant word and a first least significant word and said sine of said coarse angle to a second most significant word and a second least significant word; computing an approximation of one minus a cosine of said fine angle and an approximation of a sine of said fine angle; computing a first product by multiplying said first most significant word by said approximation of a sine of said fine angle, a second product by multiplying said first most significant word by said approximation of one minus a cosine of said fine angle, a third product by multiplying said second most significant word by said approximation of one minus a cosine of said fine angle, and a fourth product by multiplying said second most significant word by said approximation of a sine of said fine angle; and generating approximations of a cosine of said input angle modulo π/k and a sine of said input angle modulo π/k using said cosine of said coarse angle, said sine of said coarse angle, and each of said products, wherein k is an integer selected in accordance with octant or quadrant symmetry.