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A019889 Decimal expansion of sine of 80 degrees = cos(Pi/18).

%I A019889 #46 Aug 31 2025 10:07:34
%S A019889 9,8,4,8,0,7,7,5,3,0,1,2,2,0,8,0,5,9,3,6,6,7,4,3,0,2,4,5,8,9,5,2,3,0,
%T A019889 1,3,6,7,0,6,4,3,2,5,1,7,1,9,8,4,2,4,1,8,7,9,0,0,2,5,7,5,2,3,5,5,8,2,
%U A019889 7,5,9,9,9,4,3,0,3,6,2,3,9,2,7,4,6,7,8,4,1,0,0,5,6,1,1,9,8,9,9
%N A019889 Decimal expansion of sine of 80 degrees = cos(Pi/18).
%H A019889 Ivan Panchenko, <a href="/A019889/b019889.txt">Table of n, a(n) for n = 0..1000</a>
%H A019889 <a href="/index/Al#algebraic_06">Index entries for algebraic numbers, degree 6</a>
%F A019889 Equals 2F1(7/12,5/12;1/2;3/4) / 2. - _R. J. Mathar_, Oct 27 2008
%F A019889 Also the real part of I^(1/9). - _Stanislav Sykora_, Nov 29 2013
%F A019889 Equals sin(4*Pi/9). - _Wesley Ivan Hurt_, Sep 01 2014
%F A019889 Equals 2*A019849*A019859. - _R. J. Mathar_, Jan 17 2021
%F A019889 Largest positive root of 64*x^6 - 96*x^4 + 36*x^2 - 3. - _Artur Jasinski_, May 09 2025
%F A019889 Other roots are +- A019849 and +- A019829. - _R. J. Mathar_, Aug 29 2025
%F A019889 4*this^3 -3*this = A010527. - _R. J. Mathar_, Aug 29 2025
%F A019889 Equals 2F1(-1/12,1/12; 1/2 ; 3/4). - _R. J. Mathar_, Aug 31 2025
%e A019889 0.9848077530122080593667430245895230136706432517198424187900...
%p A019889 Digits:=100: evalf(sin(4*Pi/9)); # _Wesley Ivan Hurt_, Sep 01 2014
%t A019889 RealDigits[ Cos[Pi/18], 10, 111] (* _Robert G. Wilson v_ *)
%t A019889 RealDigits[Sin[80 Degree],10,120][[1]] (* _Harvey P. Dale_, Apr 16 2022 *)
%o A019889 (PARI) real(I^(1/9)) \\ _Michel Marcus_, Nov 29 2013
%Y A019889 Cf. A019849, A019859.
%K A019889 nonn,cons,changed
%O A019889 0,1
%A A019889 _N. J. A. Sloane_