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A019893 Decimal expansion of sine of 84 degrees.

%I A019893 #33 Aug 31 2025 10:09:09
%S A019893 9,9,4,5,2,1,8,9,5,3,6,8,2,7,3,3,3,6,9,2,2,6,9,1,9,4,4,9,8,0,5,7,0,3,
%T A019893 8,1,5,2,0,7,9,2,0,8,8,7,0,9,3,1,9,4,2,7,3,6,6,5,5,8,8,3,3,5,7,4,3,1,
%U A019893 6,2,5,0,6,8,6,8,9,8,3,6,2,5,7,9,3,0,6,2,2,0,3,8,3,3,6,0,9,2,9
%N A019893 Decimal expansion of sine of 84 degrees.
%C A019893 Equals sin(7*Pi/15). - _Wesley Ivan Hurt_, Sep 01 2014
%C A019893 An algebraic number of degree 8 and denominator 2. - _Charles R Greathouse IV_, Aug 27 2017
%H A019893 Ivan Panchenko, <a href="/A019893/b019893.txt">Table of n, a(n) for n = 0..1000</a>
%H A019893 Wikipedia, <a href="http://en.wikipedia.org/wiki/Exact_trigonometric_constants">Exact trigonometric constants</a>
%H A019893 <a href="/index/Al#algebraic_08">Index entries for algebraic numbers, degree 8</a>
%F A019893 Equals cos(Pi/30) = 2F1(11/20,9/20;1/2;3/4) / 2. - _R. J. Mathar_, Oct 27 2008
%F A019893 Equals 2*A019851*A019857. - _R. J. Mathar_, Jan 17 2021
%F A019893 Root of 256*x^8 -448*x^6 +224*x^4 -32*x^2 +1 = 0. - _R. J. Mathar_, Aug 29 2025
%F A019893 4*this^3 -3*this = A019881. - _R. J. Mathar_, Aug 29 2025
%F A019893 Equals 2F1(-1/20,1/20;1/2;3/4). - _R. J. Mathar_, Aug 31 2025
%e A019893 0.9945218953682733369226919449805703815207920887093194273665588...
%p A019893 Digits:=100: evalf(sin(7*Pi/15)); # _Wesley Ivan Hurt_, Sep 01 2014
%t A019893 RealDigits[ Cos[Pi/30], 10, 111] (* _Robert G. Wilson v_ *)
%t A019893 RealDigits[Sin[84 Degree],10,120][[1]] (* _Harvey P. Dale_, May 14 2022 *)
%o A019893 (PARI) cos(Pi/30) \\ _Charles R Greathouse IV_, Aug 27 2017
%K A019893 nonn,cons,changed
%O A019893 0,1
%A A019893 _N. J. A. Sloane_