A019829 Decimal expansion of sine of 20 degrees.

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

Offset

0,1

Links

Ivan Panchenko, Table of n, a(n) for n = 0..1000

Index entries for algebraic numbers, degree 6

Formula

Equals cos(7*Pi/18) = 2F1(13/12,-1/12;1/2;3/4) / 2. - R. J. Mathar, Oct 27 2008

Root of the equation 64*x^6 - 96*x^4 + 36*x^2 - 3 = 0. - Vaclav Kotesovec, Jan 19 2019 (other A019849, A019889)

Equals sqrt(8 - 2^(4/3)*(1 + i*sqrt(3))^(2/3) + i*2^(2/3)*(1 + i*sqrt(3))^(1/3)*(i + sqrt(3)))/4, where i is the imaginary unit. - Vaclav Kotesovec, Jan 19 2019

Equals 2*A019819 *A019889. - R. J. Mathar, Jan 17 2021

This^2 + A019879^2=1. - R. J. Mathar, Aug 31 2025

Example

0.34202014332566873304409961468225958076308336751416062846504849768471476...

Mathematica

RealDigits[ Sin[Pi/9], 10, 111][[1]]  (* Robert G. Wilson v *)

Prog

(PARI) /* for x = 20 degrees, sin(9x) = 0 */
/* so sin(x) is a zero of this polynomial */
sin_9(x)=9*x-120*x^3+432*x^5-576*x^7+256*x^9
x=34; y=100; print(3); print(4);
for(digits=1, 110, {d=0; y=y*10; while(sin_9((10*x+d)/y) > 0, d++);
d--; /* while loop overshoots correct digit */
print(d); x=10*x+d})
\\ Michael B. Porter, Jan 27 2010
(PARI) sin(Pi/9) \\ Charles R Greathouse IV, Feb 04 2025

Crossrefs

Cf. A323601.

Sequence in context: A332096 A077451 A352770 * A383115 A384782 A200125

Adjacent sequences: A019826 A019827 A019828 * A019830 A019831 A019832

Keyword

nonn,cons

Author

N. J. A. Sloane

Status

approved