%I #41 Aug 21 2023 10:23:38
%S 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,
%T 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,
%U 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
%N Decimal expansion of sine of 10 degrees.
%C Also the imaginary part of i^(1/9). - _Stanislav Sykora_, Apr 25 2012
%H Ivan Panchenko, <a href="/A019819/b019819.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Al#algebraic_03">Index entries for algebraic numbers, degree 3</a>
%F 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
%F From _Artur Jasinski_, Oct 28 2008: (Start)
%F Decimal expansion of root of cubic polynomial 1 - 6*x + 8*x^3.
%F Decimal expansion of casus irreducibilis:
%F (1/2) * (((-i*sqrt(3) - 1)/2)^(2/3) + ((i*sqrt(3) - 1)/2)^(2/3)). (End)
%F Equals 2 * A019814 * A019894. - _R. J. Mathar_, Jan 17 2021
%e 0.173648177...
%t First[RealDigits[Root[1 - 6 #1 + 8 #1^3 &, 2], 10, 100]] (* _Artur Jasinski_, Oct 28 2008 *)
%t RealDigits[ Sin[Pi/18], 10, 111] (* _Robert G. Wilson v_ *)
%o (PARI) sin(Pi/18) \\ _Charles R Greathouse IV_, Apr 25 2012
%K nonn,cons
%O 0,2
%A _N. J. A. Sloane_