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

Author

N. J. A. Sloane

Keywords

• nonn
• cons
• changed

Examples

			0.34202014332566873304409961468225958076308336751416062846504849768471476...
		

Links

• Ivan Panchenko, Table of n, a(n) for n = 0..1000
• Index entries for algebraic numbers, degree 6

Crossrefs

Cf. A323601.

Programs

Mathematica

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

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

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