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A019890 Decimal expansion of sine of 81 degrees.

%I A019890 #35 Aug 31 2025 10:08:34
%S A019890 9,8,7,6,8,8,3,4,0,5,9,5,1,3,7,7,2,6,1,9,0,0,4,0,2,4,7,6,9,3,4,3,7,2,
%T A019890 6,0,7,5,8,4,0,6,8,6,1,5,8,9,8,8,0,4,3,4,9,2,3,9,0,4,8,0,1,6,3,8,0,7,
%U A019890 2,9,3,5,9,6,9,7,1,2,7,3,5,7,1,1,9,6,3,0,3,7,9,9,9,8,8,6,7,7,8
%N A019890 Decimal expansion of sine of 81 degrees.
%C A019890 Also the real part of i^(1/10). - _Stanislav Sykora_, Apr 25 2012
%C A019890 Equals sin(9*Pi/20). - _Wesley Ivan Hurt_, Sep 01 2014
%C A019890 An algebraic number of degree 8 and denominator 2. - _Charles R Greathouse IV_, Aug 27 2017
%H A019890 Ivan Panchenko, <a href="/A019890/b019890.txt">Table of n, a(n) for n = 0..1000</a>
%H A019890 Wikipedia, <a href="https://en.wikipedia.org/wiki/Trigonometric_constants_expressed_in_real_radicals">Trigonometric constants expressed in real radicals</a>
%H A019890 <a href="/index/Al#algebraic_08">Index entries for algebraic numbers, degree 8</a>
%F A019890 Equals cos(Pi/20) = sqrt((1+A019881)/2) = sqrt(1-A019818^2) = sqrt(5-sqrt(5))*(sqrt(5)+sqrt(5+2*sqrt(5)))/(4*sqrt(5)). - _R. J. Mathar_, Jun 18 2006
%F A019890 Equals A019863 * A019872 + A019836 * A019845 = A019887 * A019896 + A019812 * A019821. - _R. J. Mathar_, Jan 27 2021
%F A019890 Root of 256*x^8 -512*x^6 +304*x^4 -48*x^2+1=0. - _R. J. Mathar_, Aug 29 2025
%F A019890 Equals 2F1(-1/10,1/10;1/2;1/2). - _R. J. Mathar_, Aug 31 2025
%e A019890 0.98768834059513772619004024769343726075840686158988043492390480163...
%p A019890 Digits:=100: evalf(sin(9*Pi/20)); # _Wesley Ivan Hurt_, Sep 01 2014
%t A019890 RealDigits[Sin[81 Degree],10,120][[1]] (* _Harvey P. Dale_, Aug 11 2012 *)
%o A019890 (PARI) sin(9*Pi/20) \\ _Charles R Greathouse IV_, Aug 27 2017
%K A019890 nonn,cons,changed
%O A019890 0,1
%A A019890 _N. J. A. Sloane_