Advances on the simplification of sine-cosine equations (Q1264432)

The paper is concerned with the solution or simplification of systems \(f(s,c)= 0\), \(s^2+ c^2- 1=0\). Applications are taken from the field of kinematics. The authors present fast algorithms for the functional decomposition and factorization problems, reducing the solution of the above equations (for sine-cosine polynomials) to a sequence of lower degree ones. Moreover, they show that triangularization of a given sine-cosine equation provides a conceptional understanding of the conditions that yield extraneous roots in the half-angle tangent substitution.