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Trigonometric number
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.
References
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
See also
Exact trigonometric constants
Niven's theorem
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