A019934 Decimal expansion of tangent of 36 degrees.

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

Offset

0,1

Comments

Also the decimal expansion of cotangent of 54 degrees. - Mohammad K. Azarian, Jun 30 2013

A quartic integer. - Charles R Greathouse IV, Aug 27 2017

Links

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

Wikipedia, Exact trigonometric constants.

Index entries for algebraic numbers, degree 4.

Formula

This number is sqrt(5-2*sqrt(5)). This number * A019970 = sqrt(5) = A002163. - R. J. Mathar, Jun 18 2006

The smallest positive solution of cos(4*arctan(x)) = cos(6*arctan(x)). - Thomas Olson, Oct 03 2014

Let r(n) = (n - 1)/(n + 1) if n mod 4 = 1, (n + 1)/(n - 1) otherwise; then this constant (A019934) equals with Product_{n>=0} r(10*n+5) = (2/3) * (8/7) * (12/13) * (18/17) * ... - Dimitris Valianatos, Sep 14 2019

Equals Product_{k>=1} (1 + (-1)^k/A063226(k)). - Amiram Eldar, Nov 23 2024

Equals 1/A019952. - Hugo Pfoertner, Nov 23 2024

tan(Pi/5) = A019845 / A019863. - R. J. Mathar, Aug 31 2025

Smallest positive of the 4 real-valued roots of x^4-10*x^2+5=0. (Other A019970). - R. J. Mathar, Aug 31 2025

Example

0.72654252800536088589546675748061874961609239296520...

Mathematica

RealDigits[Tan[36 Degree], 10, 120][[1]] (* Harvey P. Dale, Nov 06 2012 *)

Prog

(PARI) tan(Pi/5) \\ Charles R Greathouse IV, Aug 27 2017

Crossrefs

Cf. A019934, A019952, A019970, A002163, A063226.

Sequence in context: A225444 A379605 A175408 * A295874 A182548 A322933

Adjacent sequences: A019931 A019932 A019933 * A019935 A019936 A019937

Keyword

nonn,cons,changed

Author

N. J. A. Sloane

Status

approved