A019824 Decimal expansion of sine of 15 degrees.
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, 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, 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
Offset: 0
Examples
0.258819045102520762348898837624048328349068901319930513814003207315...
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..1000
- Mark B. Villarino, Legendre's Singular Modulus, arXiv:2002.07250 [math.HO], 2020.
- Wikipedia, Trigonometric constants expressed in real radicals
- Index entries for algebraic numbers, degree 4
Programs
-
Mathematica
RealDigits[ Sin[ Pi/12], 10, 111][[1]] (* Or *) RealDigits[(Sqrt[3] - 1)/(2 Sqrt[2]), 10, 111][[1]] (* Robert G. Wilson v *) RealDigits[Sin[15 Degree],10,120][[1]] (* Harvey P. Dale, Jul 16 2016 *)
-
PARI
sin(Pi/12) \\ Charles R Greathouse IV, Apr 25 2012
Formula
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
Equals sqrt(2 - sqrt(3))/2 = (1/2) * A101263. - Amiram Eldar, Aug 05 2020
Equals A019819 * A019894 + A019814 * A019889 = A019821 * A019896 + A019812 * A019887. - R. J. Mathar, Jan 27 2021
This^2 + A019884^2=1. - R. J. Mathar, Aug 31 2025
Smallest positive of the 4 real-valued roots of 16*x^4-16*x^2+1=0. - R. J. Mathar, Aug 31 2025
Comments