Advances on the Simplification of Sine–Cosine Equations

In this paper we contribute several results to the approach initiated by Hommel and Kovács (well documented with applications in a recent book by Kovács (1993)) on the symbolic simplification of sine–cosine polynomials that arise, for instance, as determining equations for joint values in robotics inverse kinematic problems. We present, taking into consideration for the first time sine–cosine polyomials, fast algorithms for the functional decomposition and factorization problems, reducing the solving of suchs–cequations to a sequence of lower degree ones. Moreover, we show that triangularization of a given sine–cosine equation provides a conceptual understanding of the conditions that yield extraneous roots in the half-angle tangent substitution (and therefore that imply a reduction of the degree in the determining equation of a givens–csystem).