Systems of equations with periodic functions

Seeking roots of systems of equations with periodic functions such as sine and cosine can lead to an infinite number of roots. It is important to graph the equations so that the number of intersection points can be seen. Then the periodicity of the equation can often be used to determine the infinite sequence of roots. Maple is often smart enough to give a complete set of roots within one period. Again, the approach is to use the solve command first and then use the fsolve command if the solve command fails.