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

0,1

Comments

Also the imaginary part of i^(1/6). - Stanislav Sykora, Apr 25 2012

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

Formula

Equals (sqrt(3)-1)/(2*sqrt(2)) = (A002194 -1) * A020765 = sin(Pi/12). - R. J. Mathar, Jun 18 2006

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

Equals 1/(4*A019884). - R. J. Mathar, Sep 05 2025

Example

0.258819045102520762348898837624048328349068901319930513814003207315...

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 *)

Prog

(PARI) sin(Pi/12) \\ Charles R Greathouse IV, Apr 25 2012

Crossrefs

Cf. A002194, A020765, A101263.

Sequence in context: A346180 A377995 A103311 * A284868 A019772 A356870

Adjacent sequences: A019821 A019822 A019823 * A019825 A019826 A019827

Keyword

nonn,cons

Author

N. J. A. Sloane

Status

approved