A019890 - OEIS

%I #28 Aug 21 2023 11:41:56

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

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

%U 2,9,3,5,9,6,9,7,1,2,7,3,5,7,1,1,9,6,3,0,3,7,9,9,9,8,8,6,7,7,8

%N Decimal expansion of sine of 81 degrees.

%C Also the real part of i^(1/10). - _Stanislav Sykora_, Apr 25 2012

%C Equals sin(9*Pi/20). - _Wesley Ivan Hurt_, Sep 01 2014

%C An algebraic number of degree 8 and denominator 2. - _Charles R Greathouse IV_, Aug 27 2017

%H Ivan Panchenko, <a href="/A019890/b019890.txt">Table of n, a(n) for n = 0..1000</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Trigonometric_constants_expressed_in_real_radicals">Trigonometric constants expressed in real radicals</a>

%H <a href="/index/Al#algebraic_08">Index entries for algebraic numbers, degree 8</a>

%F Equals cos(Pi/20) = sqrt((1+A019881)/2) = sqrt(1-A019818^2) = sqrt(5-sqrt(5))*(sqrt(5)+sqrt(5+2*sqrt(5)))/(4*sqrt(5)). - _R. J. Mathar_, Jun 18 2006

%F Equals A019863 * A019872 + A019836 * A019845 = A019887 * A019896 + A019812 * A019821. - _R. J. Mathar_, Jan 27 2021

%e 0.98768834059513772619004024769343726075840686158988043492390480163...

%p Digits:=100: evalf(sin(9*Pi/20)); # _Wesley Ivan Hurt_, Sep 01 2014

%t RealDigits[Sin[81 Degree],10,120][[1]] (* _Harvey P. Dale_, Aug 11 2012 *)

%o (PARI) sin(9*Pi/20) \\ _Charles R Greathouse IV_, Aug 27 2017

%K nonn,cons

%O 0,1

%A _N. J. A. Sloane_.