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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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