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A019884 Decimal expansion of sine of 75 degrees.

%I A019884 #48 Aug 31 2025 11:23:00
%S A019884 9,6,5,9,2,5,8,2,6,2,8,9,0,6,8,2,8,6,7,4,9,7,4,3,1,9,9,7,2,8,8,9,7,3,
%T A019884 6,7,6,3,3,9,0,4,8,3,9,0,0,8,4,0,4,5,5,0,4,0,2,3,4,3,0,7,6,3,1,0,4,2,
%U A019884 3,2,1,3,9,7,9,8,5,5,5,1,6,3,4,7,5,6,1,7,4,1,8,5,8,0,7,0,4,5,1
%N A019884 Decimal expansion of sine of 75 degrees.
%C A019884 Also the real part of i^(1/6). - _Stanislav Sykora_, Apr 25 2012
%C A019884 Length of one side of the new Type 15 Convex Pentagon. - _Michel Marcus_, Aug 04 2015
%H A019884 Vincenzo Librandi, <a href="/A019884/b019884.txt">Table of n, a(n) for n = 0..1000</a>
%H A019884 Casey Mann et al, <a href="http://i.imgur.com/AyDuinZ.png">Type 15 Convex Pentagon</a>, Jul 29 2015.
%H A019884 Wikipedia, <a href="https://en.wikipedia.org/wiki/Trigonometric_constants_expressed_in_real_radicals">Trigonometric constants expressed in real radicals</a>.
%H A019884 <a href="/index/Al#algebraic_04">Index entries for algebraic numbers, degree 4</a>
%F A019884 Equals cos(Pi/12) = [1+sqrt(3)]/[2*sqrt(2)] = A090388 * A020765. - _R. J. Mathar_, Jun 18 2006
%F A019884 Equals A019859 * A019874 + A019834 * A019849 = A019881 * A019896 + A019812 * A019827 . - _R. J. Mathar_, Jan 27 2021
%F A019884 Equals 1/(sqrt(6) - sqrt(2)) = 1/A120683. - _Amiram Eldar_, Aug 04 2022
%F A019884 Largest of the 4 real-valued roots of 16*x^4 -16*x^2 +1=0. - _R. J. Mathar_, Aug 29 2025
%F A019884 4*this^3 -3*this = A010503. - _R. J. Mathar_, Aug 29 2025
%F A019884 Equals 2F1(-1/8,1/8 ;1/2;3/4) = 2F1(-1/6,1/6;1/2;1/2). - _R. J. Mathar_, Aug 31 2025
%e A019884 0.96592582628906828674974319972889736763390483900840455040234307631042...
%t A019884 RealDigits[Sin[75 Degree], 10, 100][[1]] (* _Vincenzo Librandi_, Aug 11 2014 *)
%o A019884 (PARI) cos(Pi/12) \\ _Charles R Greathouse IV_, Apr 25 2012
%Y A019884 Cf. A120683.
%K A019884 nonn,cons,changed
%O A019884 0,1
%A A019884 _N. J. A. Sloane_