Trigonometric Functions and the Sensations of Tone

Abstract

Music provides an excellent setting for students to explore trigonometric functions in a setting which is independent of their utility in resolving triangles. In this paper, we present several investigations using trigonometric functions to model musical phenomena. From a mathematical technology point of view, most examples require only function graphing and can be explored using a modern interactive graphing application. One example, however, is an excellent application of trigonometric simplification, for which a Computer Algebra System is a useful tool. A final application is suitable for calculus students and provides an exercise in integration by parts. This can be done by hand, or with the aid of an algebra system.