Journal of Integer Sequences, Vol. 21 (2018), Article 18.9.5

Minimal Polynomials of Algebraic Cosine Values, II

Pinthira Tangsupphathawat
Department of Mathematics
Phranakhon Rajabhat University
Bangkok 10220

Takao Komatsu
School of Mathematics and Statistics
Wuhan University
Wuhan 430072

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


We derive alternative proofs of two recent results due to Gürtas, and a new recursion related to the minimal polynomials of algebraic cosine values. We determine the minimal polynomials of algebraic values of the sine function evaluated at rational multiples of π. We also correct a formula from our earlier work.

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(Concerned with sequences A000010 A023022 A178182.)

Received March 31 2017; revised versions received January 6 2018; April 20 2018; September 3 2018. Published in Journal of Integer Sequences, December 10 2018.

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