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

0,1

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

Links

Zak Seidov, Table of n, a(n) for n = 0..999

Wikipedia, Exact trigonometric constants

Index entries for algebraic numbers, degree 4

Formula

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

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

Example

sin 36 degrees = 0.587785252292473129168705954639...

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A230366 A358361 A197415 * A357838 A143618 A177056

Adjacent sequences: A019842 A019843 A019844 * A019846 A019847 A019848

Keyword

nonn,cons,easy

Author

N. J. A. Sloane

Status

approved