A simple proof of the transcendence of the trigonometric functions

2019/12/11 by Yuanyuan Lian, Kai Zhang, Lian, Yuanyuan +1
Mathematics · #11J81 #FOS: Mathematics #Mathematics and Applications #Number Theory (math.NT) #math.NT #msc:11J81

paper · pdf · doi:10.48550/arxiv.1912.05348

arxiv created 2019/12/11 · openalex publication_date 2019/12/11 · arxiv updated 2019/12/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note, we give a simple proof that the values of the trigonometric functions at any nonzero rational number are transcendental numbers.

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