Algebraic relations between sine and cosine values
Number Theory
2024-06-04 v1
Abstract
The aim of this note is to show that any algebraic relation over between the values of the trigonometric functions sine and cosine at algebraic points can be derived from the Pythagorean identity and the angle addition formulas. This result is obtained as a consequence of the Lindemann-Weierstrass theorem.
Cite
@article{arxiv.2406.01296,
title = {Algebraic relations between sine and cosine values},
author = {B. Adamczewski and É. Delaygue},
journal= {arXiv preprint arXiv:2406.01296},
year = {2024}
}
Comments
Accepted for publication in The American Mathematical Monthly