Journal of Integer Sequences, Vol. 19 (2016), Article 16.2.8

Minimal Polynomials of Algebraic Cosine Values at Rational Multiples of π

Pinthira Tangsupphathawat
Department of Mathematics
Phranakhon Rajabhat University
Bangkok 10220

Vichian Laohakosol
Department of Mathematics
Faculty of Science
Kasetsart University
Bangkok 10900


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

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Received February 8 2016. Revised version received March 15 2016. Published in Journal of Integer Sequences, March 19 2016.

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