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%I #42 Aug 21 2023 12:24:20
%S 2,5,8,8,1,9,0,4,5,1,0,2,5,2,0,7,6,2,3,4,8,8,9,8,8,3,7,6,2,4,0,4,8,3,
%T 2,8,3,4,9,0,6,8,9,0,1,3,1,9,9,3,0,5,1,3,8,1,4,0,0,3,2,0,7,3,1,5,0,5,
%U 6,9,7,4,7,4,8,8,0,1,9,9,6,9,2,2,3,6,7,9,7,4,6,9,4,2,4,9,6,6,5
%N Decimal expansion of sine of 15 degrees.
%C Also the imaginary part of i^(1/6). - _Stanislav Sykora_, Apr 25 2012
%H Vincenzo Librandi, <a href="/A019824/b019824.txt">Table of n, a(n) for n = 0..1000</a>
%H Mark B. Villarino, <a href="https://arxiv.org/abs/2002.07250">Legendre's Singular Modulus</a>, arXiv:2002.07250 [math.HO], 2020.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Trigonometric_constants_expressed_in_real_radicals">Trigonometric constants expressed in real radicals</a>
%H <a href="/index/Al#algebraic_04">Index entries for algebraic numbers, degree 4</a>
%F Equals (sqrt(3)-1)/(2*sqrt(2)) = (A002194 -1) * A020765 = sin(Pi/12). - _R. J. Mathar_, Jun 18 2006
%F Equals 2F1(9/8,-1/8;1/2;3/4) / 2 = - 2F1(11/8,-3/8;1/2;3/4) / 2 = cos(5*Pi/12). - _R. J. Mathar_, Oct 27 2008
%F Equals sqrt(2 - sqrt(3))/2 = (1/2) * A101263. - _Amiram Eldar_, Aug 05 2020
%F Equals A019819 * A019894 + A019814 * A019889 = A019821 * A019896 + A019812 * A019887. - _R. J. Mathar_, Jan 27 2021
%e 0.258819045102520762348898837624048328349068901319930513814003207315...
%t RealDigits[ Sin[ Pi/12], 10, 111][[1]] (* Or *) RealDigits[(Sqrt[3] - 1)/(2 Sqrt[2]), 10, 111][[1]] (* _Robert G. Wilson v_ *)
%t RealDigits[Sin[15 Degree],10,120][[1]] (* _Harvey P. Dale_, Jul 16 2016 *)
%o (PARI) sin(Pi/12) \\ _Charles R Greathouse IV_, Apr 25 2012
%Y Cf. A002194, A020765, A101263.
%K nonn,cons
%O 0,1
%A _N. J. A. Sloane_