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A019887 Decimal expansion of sine of 78 degrees.

%I A019887 #32 Aug 31 2025 11:42:52
%S A019887 9,7,8,1,4,7,6,0,0,7,3,3,8,0,5,6,3,7,9,2,8,5,6,6,7,4,7,8,6,9,5,9,9,5,
%T A019887 3,2,4,5,9,7,3,7,8,0,8,8,6,2,6,7,7,1,0,7,8,8,5,1,7,7,6,6,3,6,4,0,5,9,
%U A019887 6,8,3,3,1,2,0,0,9,5,1,2,1,9,9,9,7,5,8,5,2,5,4,5,4,7,8,5,6,3,6
%N A019887 Decimal expansion of sine of 78 degrees.
%C A019887 Equals sin(13*Pi/30). - _Wesley Ivan Hurt_, Aug 31 2014
%C A019887 A quartic number with denominator 2 and minimal polynomial 16x^4 + 8x^3 - 16x^2 - 8x + 1. - _Charles R Greathouse IV_, Aug 27 2017
%H A019887 Ivan Panchenko, <a href="/A019887/b019887.txt">Table of n, a(n) for n = 0..1000</a>
%H A019887 Wikipedia, <a href="http://en.wikipedia.org/wiki/Exact_trigonometric_constants">Exact trigonometric constants</a>
%H A019887 <a href="/index/Al#algebraic_04">Index entries for algebraic numbers, degree 4</a>
%F A019887 Equals cos(Pi/15) = [sqrt(5)-1]*[1+sqrt(3)*sqrt{5+2*sqrt(5)}]/8 = [A002163-1]*[1+A002194*A019970]/8. - _R. J. Mathar_, Jun 18 2006
%F A019887 Equals 2*A019848*A019860. - _R. J. Mathar_, Jan 17 2021
%F A019887 4*this^3 -3*this = A019863. - _R. J. Mathar_, Aug 29 2025
%F A019887 Equals 2F1(-1/10,1/10 ; 1/2 ; 3/4). - _R. J. Mathar_, Aug 31 2025
%F A019887 A root of 16*x^4+8*x^3-16*x^2-8*x+1=0. - _R. J. Mathar_, Aug 31 2025
%e A019887 0.9781476007338056379285667478695995324597378088626771078851...
%p A019887 Digits:=100: evalf(sin(13*Pi/30)); # _Wesley Ivan Hurt_, Aug 31 2014
%t A019887 First@RealDigits[Sin[78 Degree], 10, 120] (* _Michael De Vlieger_, Aug 31 2014 *)
%o A019887 (PARI) cos(Pi/15) \\ _Charles R Greathouse IV_, Aug 27 2017
%K A019887 nonn,cons,changed
%O A019887 0,1
%A A019887 _N. J. A. Sloane_