A019887 Decimal expansion of sine of 78 degrees.

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

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• cons
• changed

Comments

Equals sin(13*Pi/30). - Wesley Ivan Hurt, Aug 31 2014

A quartic number with denominator 2 and minimal polynomial 16x^4 + 8x^3 - 16x^2 - 8x + 1. - Charles R Greathouse IV, Aug 27 2017

Examples

			0.9781476007338056379285667478695995324597378088626771078851...
		

Links

• Ivan Panchenko, Table of n, a(n) for n = 0..1000
• Wikipedia, Exact trigonometric constants
• Index entries for algebraic numbers, degree 4

Programs

Maple

Digits:=100: evalf(sin(13*Pi/30)); # Wesley Ivan Hurt, Aug 31 2014

Mathematica

First@RealDigits[Sin[78 Degree], 10, 120] (* Michael De Vlieger, Aug 31 2014 *)

PARI

cos(Pi/15) \\ Charles R Greathouse IV, Aug 27 2017

Formula

Equals cos(Pi/15) = [sqrt(5)-1]*[1+sqrt(3)*sqrt{5+2*sqrt(5)}]/8 = [A002163-1]*[1+A002194*A019970]/8. - R. J. Mathar, Jun 18 2006

Equals 2*A019848*A019860. - R. J. Mathar, Jan 17 2021

4*this^3 -3*this = A019863. - R. J. Mathar, Aug 29 2025