Sines, Cosines, and Conjugates

Author

Caleb John Hallauer

Date of Award

2005

Document Type

Undergraduate Thesis

Department

Mathematics

First Advisor

William Staton

Relational Format

Dissertation/Thesis

Abstract

This thesis is an investigation of angles whose sine and cosine are algebraic conjugates over the field of rational numbers. That is to say, sin(0) and cos(0) are roots of the same irreducible polynomial with integer coefficients. These interesting families are explored. First, it is shown that for n>2, the angles have this property. Second, all angles which are conjugate in this sense and which have a quadratic minimum polynomial are identified. The relationship between these two families is explored, and a family of conjugate angles with 4^^ degree minimum polynomials is explored as well. Questions for further investigation are proposed, including an intriguing connection to chaos theory.

Recommended Citation

Hallauer, Caleb John, "Sines, Cosines, and Conjugates" (2005). Honors Theses. 2019.
https://egrove.olemiss.edu/hon_thesis/2019

Accessibility Status

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