Algebraic relations between sine and cosine values
arXiv:2406.01296
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.
Accepted for publication in The American Mathematical Monthly