English

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 Q\overline{\mathbb{Q}} 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

R2 v1 2026-06-28T16:51:04.837Z