  In an earlier article [3], we presented an algorithm that can be used to
rigorously check whether a specific cosine or sine polynomial is nonnegative in
a given interval or not. The algorithm proves to be an indispensable tool in
establishing some recent results on nonnegative trigonometric polynomials. See,
for example, [2], [4] and [5]. It continues to play an essential role in
several ongoing projects. The algorithm, however, cannot handle general
trigonometric polynomials that involve both cosine and sine terms. Some ad hoc
methods to deal with such polynomials have been suggested in [3], but none are,
in general, satisfactory. This note supplements [3] by presenting an algorithm
applicable to all general trigonometric polynomials. It is based on the
classical Sturm Theorem, just like the earlier algorithm. A couple of the
references in [3] are also updated.
