A019827 Decimal expansion of sin(Pi/10) (angle of 18 degrees).

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

Offset

0,1

Comments

Decimal expansion of cos(2*Pi/5) (angle of 72 degrees).

Also the imaginary part of i^(1/5). - Stanislav Sykora, Apr 25 2012

One of the two roots of 4x^2 + 2x - 1 (the other is the sine of 54 degrees times -1). - Alonso del Arte, Apr 25 2015

This is the height h of the isosceles triangle in a regular pentagon inscribed in a unit circle, formed by a diagonal as base and two adjacent radii. h = cos(2*Pi/5) = sin(Pi/10). - Wolfdieter Lang, Jan 08 2018

Quadratic number of denominator 2 and minimal polynomial 4x^2 + 2x - 1. - Charles R Greathouse IV, May 13 2019

Links

Zak Seidov, Table of n, a(n) for n = 0..999

Hideyuki Ohtsuka, Problem B-1237, Elementary Problems and Solutions, The Fibonacci Quarterly, Vol. 56, No. 4 (2018), p. 366; A Telescoping Product, Solution to Problem B-1237 by Steve Edwards, ibid., Vol. 57, No. 4 (2019), pp. 369-370.

Wikipedia, Exact trigonometric constants.

Index entries for algebraic numbers, degree 2

Formula

Equals (sqrt(5) - 1)/4 = (phi - 1)/2 = 1/(2*phi), with phi from A001622.

Equals 1/(1 + sqrt(5)). - Omar E. Pol, Nov 15 2007

Equals 1/A134945. - R. J. Mathar, Jan 17 2021

Equals 2*A019818*A019890. - R. J. Mathar, Jan 17 2021

Equals Product_{k>=1} 1 - 1/(phi + phi^k), where phi is the golden ratio (A001622) (Ohtsuka, 2018). - Amiram Eldar, Dec 02 2021

Example

0.30901699437494742410229341718281905886015458990288143106772431135263...

Mathematica

RealDigits[Sin[18 Degree], 10, 108][[1]] (* Alonso del Arte, Apr 20 2015 *)

Prog

(PARI) sin(Pi/10) \\ Charles R Greathouse IV, Feb 03 2015
(PARI) polrootsreal(4*x^2 + 2*x - 1)[2] \\ Charles R Greathouse IV, Feb 03 2015

Crossrefs

Cf. A001622, A019845, A019863.

Sequence in context: A287632 A259346 A239798 * A329284 A269557 A201581

Adjacent sequences: A019824 A019825 A019826 * A019828 A019829 A019830

Keyword

nonn,cons,easy

Author

N. J. A. Sloane

Status

approved