Exact Expressions for Trigonometric Functions

Summary

Solving polynomial equations and trigonometry are typically taught in separate modules or even separate classes. The derivation of a one-third angle formula gives students the opportunity to tie these two topics together. An algorithm for finding the cosine of one-third of a prescribed angle is based on Cardano’s formula. In addition, we show how this algorithm can be combined with half, double, and triple angle formulas to give exact expressions for trigonometric functions written in terms of radicals for an infinite number of angles between 0 and $\pi /2$.

Additional information

Notes on contributors

S H Sathish Indika

S H Sathish Indika ([email protected]), originally from Sri Lanka, received his Ph.D. in Computational Applied Mathematics from Old Dominion University. He is an Associate Professor of Mathematics at Virginia Peninsula Community College. He enjoys traveling and listening to music.

Lawrence M. Leemis

Lawrence M. Leemis ([email protected]) received his B.S., M.S. and Ph.D. from Purdue University, and is currently a faculty member in the Department of Mathematics at William & Mary. He enjoys photography and riding recumbent bicycles.