Honors Theses

Date of Award


Document Type

Undergraduate Thesis



First Advisor

William Staton

Relational Format



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.

Accessibility Status

Searchable text



To view the content in your browser, please download Adobe Reader or, alternately,
you may Download the file to your hard drive.

NOTE: The latest versions of Adobe Reader do not support viewing PDF files within Firefox on Mac OS and if you are using a modern (Intel) Mac, there is no official plugin for viewing PDF files within the browser window.