Tangsupphathawat, Pinthira; Laohakosol, Vichian

Minimal polynomials of algebraic cosine values at rational multiples of $\pi $

J. Integer Seq. 19(2), Article 16.2.8, 8 p., electronic only (2016)

Summary

Summary: Lehmer proved that the values of the cosine function evaluated at rational multiples of $\pi $ are algebraic numbers. We show how to determine explicit, closed form expressions for the minimal polynomials of these algebraic numbers.

Mathematics Subject Classification

11R04, 33B10, 11J72

Keywords/Phrases

cosine function, algebraic value, multiple of pi

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