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 A019827 Decimal expansion of sin(Pi/10) (angle of 18 degrees). 22
 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 (list; constant; graph; refs; listen; history; text; internal format)
 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

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