A019819 Decimal expansion of sine of 10 degrees.

1, 7, 3, 6, 4, 8, 1, 7, 7, 6, 6, 6, 9, 3, 0, 3, 4, 8, 8, 5, 1, 7, 1, 6, 6, 2, 6, 7, 6, 9, 3, 1, 4, 7, 9, 6, 0, 0, 0, 3, 7, 5, 6, 7, 7, 1, 8, 4, 0, 6, 9, 3, 8, 7, 2, 3, 6, 2, 4, 1, 3, 7, 8, 1, 3, 2, 0, 6, 5, 8, 2, 2, 1, 3, 9, 0, 1, 4, 7, 3, 5, 4, 2, 1, 5, 1, 6, 6, 1, 3, 1, 5, 7, 3, 9, 9, 5, 7, 4

Offset

0,2

Comments

Also the imaginary part of i^(1/9). - Stanislav Sykora, Apr 25 2012

Links

Ivan Panchenko, Table of n, a(n) for n = 0..1000

Vladimir Ivanovich Smirnov, A course of higher mathematics, vol. 1, Pergamon Press, 1964, p. 342.

Index entries for algebraic numbers, degree 3.

Formula

Equals cos(4*Pi/9) = 2F1(7/6,-1/6;1/2;3/4) / 2 = - 2F1(4/3,-1/3;1/2;3/4) / 2. - R. J. Mathar, Oct 27 2008

From Artur Jasinski, Oct 28 2008: (Start)

Decimal expansion of root of cubic polynomial 1 - 6*x + 8*x^3. (Others A019859, -A019879)

Decimal expansion of casus irreducibilis:

(1/2) * (((-i*sqrt(3) - 1)/2)^(2/3) + ((i*sqrt(3) - 1)/2)^(2/3)). (End)

Equals 2 * A019814 * A019894. - R. J. Mathar, Jan 17 2021

This^2 + A019889^2 = 1. - R. J. Mathar, Aug 31 2025

Equals A019829/(2*A019889). - R. J. Mathar, Sep 05 2025

Equals (1/2)*Sum_{k>=0} binomial(3*k+1, k)*3^(-3*k-1)/(3*k+1). - Stefano Spezia, Dec 23 2025

Example

0.173648177...

Mathematica

First[RealDigits[Root[1 - 6 #1 + 8 #1^3 &, 2], 10, 100]] (* Artur Jasinski, Oct 28 2008 *)
RealDigits[ Sin[Pi/18], 10, 111]  (* Robert G. Wilson v *)

Prog

(PARI) sin(Pi/18) \\ Charles R Greathouse IV, Apr 25 2012

Crossrefs

Cf. A019814.

Sequence in context: A091682 A073016 A238695 * A215693 A197028 A392302

Adjacent sequences: A019816 A019817 A019818 * A019820 A019821 A019822

Keyword

nonn,cons

Author

N. J. A. Sloane

Status

approved