International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 63, Pages 3419-3422

On polynomials with simple trigonometric formulas

R. J. Gregorac

Department of Mathematics, Iowa State University, Ames 50011, IA, USA

Received 19 November 2003

Copyright © 2004 R. J. Gregorac. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We show that the sequences of polynomials with zeros cot(mπ/(n+2)) and tan(mπ/(n+2)) are not orthogonal sequences with respect to any integral inner product. We give an algebraic formula for these polynomials, that is simpler than the formula originally derived by Cvijovic and Klinowski (1998). New sequences of polynomials with algebraic numbers as roots and closed trigonometric formulas are also derived by these methods.