English

A New Approach to Rational Values of Trigonometric Functions

History and Overview 2009-09-01 v2 Number Theory

Abstract

It is well known that sin(a\pi/b), cos(a\pi/b), etc., are only rational numbers for a few select integers a and b. We show that this is equivalent to the fact that only for d = 1,2,3,4, and 6 is the primitive dth root of unity of degree 2 over Q.

Keywords

Cite

@article{arxiv.0904.0826,
  title  = {A New Approach to Rational Values of Trigonometric Functions},
  author = {Gregory P. Dresden},
  journal= {arXiv preprint arXiv:0904.0826},
  year   = {2009}
}

Comments

4 pages, 2 figures, 5 references, with new 6th reference to an easier proof of my result

R2 v1 2026-06-21T12:48:24.811Z