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A019829 Decimal expansion of sine of 20 degrees. 4
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 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

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

FORMULA

Equals cos(7*Pi/18) = 2F1(13/12,-1/12;1/2;3/4) / 2 . [From 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

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

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

CROSSREFS

Cf. A323601.

Sequence in context: A167876 A241833 A077451 * A200125 A091528 A236679

Adjacent sequences:  A019826 A019827 A019828 * A019830 A019831 A019832

KEYWORD

nonn,cons

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified February 22 05:52 EST 2020. Contains 332116 sequences. (Running on oeis4.)