Functional Equations with Trigonometric Function Solutions

Abstract

This article aims to treat the problem of characterizing the trigonometric sine and cosine function. Our method arises from Kannappan’s work of 2003 which solved the functional equation for functions whose domain is a group and whose range is a subset of the complex field without any additional conditions. We use Kannappan’s technique to determine the general solutions of the functional equation which, together with Kannappan’s result, give a complete characterization of the trigonometric sine and cosine functions.