A019859 Decimal expansion of sine of 50 degrees.

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

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• cons

Comments

A cubic number with denominator 2 and minimal polynomial 8x^3 - 6x + 1. - Charles R Greathouse IV, Nov 05 2017

The roots of the polynomial 8x^3 - 6x + 1 can be constructed using the intersection of the circle defined by x^(2) + y^(2) - 0.125x + 0.25y = 0.75 and the hyperbola defined by -8xy+y=-1. The circle and the hyperbola intersect at (0,-1) and 3 other points. 3 lines can be drawn by connecting the point (0,-1) to the other 3 points of intersection. The 3 lines intersect the x-axis at the locations of the roots. - Raul Prisacariu, Jul 29 2024

Examples

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Links

• Ivan Panchenko, Table of n, a(n) for n = 0..1000
• Raul Prisacariu, The Nonagon, Hyperbola and Lill’s Method
• Index entries for algebraic numbers, degree 3

Programs

Mathematica

RealDigits[ Cos[ 2Pi/9], 10, 111][[1]] (* Robert G. Wilson v *)
RealDigits[Sin[50 Degree],10,120][[1]] (* Harvey P. Dale, Dec 19 2012 *)

PARI

sin(5/18*Pi) \\ Charles R Greathouse IV, Nov 05 2017

Formula

Equals cos(2*Pi/9) = 2F1(5/6,1/6;1/2;3/4) / 2. - R. J. Mathar, Oct 27 2008

Equals 2*A019834*A019874. - R. J. Mathar, Jan 17 2021