A019819 Decimal expansion of sine of 10 degrees.
1, 7, 3, 6, 4, 8, 1, 7, 7, 6, 6, 6, 9, 3, 0, 3, 4, 8, 8, 5, 1, 7, 1, 6, 6, 2, 6, 7, 6, 9, 3, 1, 4, 7, 9, 6, 0, 0, 0, 3, 7, 5, 6, 7, 7, 1, 8, 4, 0, 6, 9, 3, 8, 7, 2, 3, 6, 2, 4, 1, 3, 7, 8, 1, 3, 2, 0, 6, 5, 8, 2, 2, 1, 3, 9, 0, 1, 4, 7, 3, 5, 4, 2, 1, 5, 1, 6, 6, 1, 3, 1, 5, 7, 3, 9, 9, 5, 7, 4
Offset: 0
Examples
0.173648177...
Links
- Ivan Panchenko, Table of n, a(n) for n = 0..1000
- Vladimir Ivanovich Smirnov, A course of higher mathematics, vol. 1 , Pergamon Press, 1964, p. 342.
- Index entries for algebraic numbers, degree 3.
Crossrefs
Cf. A019814.
Programs
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Mathematica
First[RealDigits[Root[1 - 6 #1 + 8 #1^3 &, 2], 10, 100]] (* Artur Jasinski, Oct 28 2008 *) RealDigits[ Sin[Pi/18], 10, 111] (* Robert G. Wilson v *)
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PARI
sin(Pi/18) \\ Charles R Greathouse IV, Apr 25 2012
Formula
Equals cos(4*Pi/9) = 2F1(7/6,-1/6;1/2;3/4) / 2 = - 2F1(4/3,-1/3;1/2;3/4) / 2. - R. J. Mathar, Oct 27 2008
From Artur Jasinski, Oct 28 2008: (Start)
Decimal expansion of casus irreducibilis:
(1/2) * (((-i*sqrt(3) - 1)/2)^(2/3) + ((i*sqrt(3) - 1)/2)^(2/3)). (End)
This^2 + A019889^2 = 1. - R. J. Mathar, Aug 31 2025
Comments