A019859 - OEIS

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

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OFFSET

0,1

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

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

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

EXAMPLE

0.76604444...

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 *)