  Mixed trigonometric-polynomials frequently occur in applications in physics,
numerical analysis and engineering, the algorithm has been already proposed to
determine its sign on (0,{pi}/2]. This paper proposes a procedure to extend the
interval to (0, +{\inf}). Such generalization is by no means trivial, for the
process depends on boundedness of roots and square-free factorization of mixed
trigonometric-polynomials.
