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

Author

N. J. A. Sloane

Keywords

• nonn
• cons
• changed

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

Examples

			0.72654252800536088589546675748061874961609239296520...
		

Links

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

Crossrefs

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

Programs

Mathematica

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

PARI

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

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