A Generalisation of Niven's Theorem for Trigonometric Functions

Adam Keilthy, Ailbhe Ní Ruairí

Niven's Theorem asserts that $\{\cos (r\pi )|r\in \mathbb{Q}\}\cap \mathbb{Q}=\{0,\pm 1,\pm \frac{1}{2}\}$. This paper uses elementary methods to classify all elements in the sets $\…