In mathematics, a trigonometric number is an irrational number produced by taking the sine or cosine of a rational multiple of a circle, or equivalently, the sine or cosine in radians of a rational multiple of π, or the sine or cosine of a rational number of degrees.
Ivan Niven gave proofs of theorems regarding these numbers in Numbers: Rational and Irrational published in 1961. Li Zhou and Lubomir Markov recently improved and simplified Niven's proofs in the book.
- Li Zhou and Lubomir Markov (2010). "Recurrent Proofs of the Irrationality of Certain Trigonometric Values". American Mathematical Monthly 117 (4): 360–362. doi:10.4169/000298910x480838. http://arxiv.org/abs/0911.1933
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