A019845 Decimal expansion of sine of 36 degrees.

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

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• cons
• easy
• changed

Comments

This sequence is also decimal expansion of cosine of 54 degrees. - Mohammad K. Azarian, Jun 29 2013

The ratio of side to longer diagonal for any golden rhombus (see A019881). - Rick L. Shepherd, Apr 10 2017

Perimeter length of a regular pentagon with circumscribed unit circle. - R. J. Mathar, Aug 24 2023

Examples

			sin 36 degrees = 0.587785252292473129168705954639...
		

Links

• Zak Seidov, Table of n, a(n) for n = 0..999
• Wikipedia, Exact trigonometric constants
• Index entries for algebraic numbers, degree 4

Crossrefs

Cf. A019827 (sine of 18 degrees), A019881 (sine of 72 degrees), A001622 (golden ratio phi). A182007.

Programs

Mathematica

RealDigits[Sin[Pi/5], 10, 100][[1]] (* Alonso del Arte, Sep 19 2017 *)
RealDigits[Sin[36 Degree],10,120][[1]] (* Harvey P. Dale, Aug 14 2018 *)

PARI

sin(Pi/5) \\ Michel Marcus, Apr 25 2015

PARI

cos(3*Pi/10) \\ Rick L. Shepherd, Apr 10 2017

PARI

real(I^(3/5)) \\ Rick L. Shepherd, Apr 10 2017

Formula

sin 36 degrees = sin Pi/5 radians = sqrt((1/8)(5 - sqrt(5))) = sqrt(A187798/2).

Equals A019881/A001622. - Rick L. Shepherd, Apr 10 2017

This constant is (1/2)*A182007. - Wolfdieter Lang, May 08 2018

Equals 2*A019827*A019881. - R. J. Mathar, Jan 17 2021

Equals 5*A182007. - R. J. Mathar, Aug 24 2023

Equals cos(3*Pi/10). - R. J. Mathar, Aug 29 2025

Root of 16*x^4-20*x^2+5=0. Other 2 roots are +- A019881. - R. J. Mathar, Aug 29 2025

This^2+A019863^2=1. - R. J. Mathar, Aug 31 2025