A019818 Decimal expansion of sine of 9 degrees.

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

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• cons
• changed

Comments

Also the imaginary part of i^(1/10). - Stanislav Sykora, Apr 25 2012

An algebraic number of degree 8 and denominator 2. - Charles R Greathouse IV, Aug 27 2017

Examples

			sin(Pi/20) = 0.1564344650402308690101053194671668923138...
		

Links

• Ivan Panchenko, Table of n, a(n) for n = 0..1000
• Wikipedia, Exact trigonometric constants
• Index entries for algebraic numbers, degree 8

Crossrefs

Cf. A019812, A019815, A019893, A019896.

Programs

Mathematica

RealDigits[Sin[9 Degree],10,120][[1]] (* Harvey P. Dale, Sep 15 2014 *)

PARI

sin(Pi/20) \\ Charles R Greathouse IV, Aug 27 2017

Formula

sqrt(8-2*sqrt(10+2*sqrt(5)))/4 = sqrt((1/2)*(1 - sqrt((1/8)*(5 + sqrt(5))))). - Herman Jamke (hermanjamke(AT)fastmail.fm), Nov 13 2006

Equals A019815*A019896 + A019812*A019893. - R. J. Mathar, Jan 27 2021

This^2 + A019890^2=1. - R. J. Mathar, Aug 31 2025

Smallest positive of the 8 real-values roots of 256*x^8 -512*x^6 +304*x^4 -48*x^2+1=0. - R. J. Mathar, Aug 31 2025