We employ sinusoidal basis functions together with R.W.P. King's analytical Green functions in a Method of Moments formulation of electromagnetic scattering by thin wire mesh structures located over a dielectric ground. The present formulation is an extension of an earlier work by the authors where they have implemented R.W.P. King's Green functions for the first time in literature for the same problem using pulse basis functions. Over a number of numerical tests for canonical structures, it is observed that the results of the present formulation match perfectly with the same solutions provided by the famous open software NEC-2. While the developed codes equally have the ability to read NEC-2 formatted input files, their main advantage lies in the capability to evolve by proper substitutions of Green functions to take into account various terrain features in any scenario.