A019970 Decimal expansion of tangent of 72 degrees.

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

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• cons

Comments

Also the decimal expansion of cotangent of 18 degrees. - Mohammad K. Azarian, Jun 30 2013

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

Length of the second longest diagonal in a regular 10-gon with unit side. - Mohammed Yaseen, Nov 12 2020

Examples

			3.077683537175253402570290576036909824006702143537792427...
		

Links

• Ivan Panchenko, Table of n, a(n) for n = 1..1000
• Wikipedia, Exact trigonometric constants.
• Index entries for algebraic numbers, degree 4

Crossrefs

Cf. A019881 (sine of 72 degrees).

Cf. A019904, A019934, A019964.

Programs

Magma

SetDefaultRealField(RealField(100)); Sqrt(5+2*Sqrt(5)); // G. C. Greubel, Nov 21 2018

Mathematica

RealDigits[Tan[72 Degree],10,120][[1]] (* Harvey P. Dale, Apr 30 2012 *)
RealDigits[Sqrt[5 + 2*Sqrt[5]], 10, 100][[1]] (* G. C. Greubel, Nov 21 2018 *)

PARI

tan(2*Pi/5) \\ Charles R Greathouse IV, Aug 27 2017

Sage

numerical_approx(tan(2*pi/5), digits=100) # G. C. Greubel, Nov 21 2018

Formula

Equals sqrt(5 + 2*sqrt(5)). - R. J. Mathar, Jun 18 2006

Equals tan(66 degrees) + tan(36 degrees) + tan(6 degrees). - Amiram Eldar, Apr 07 2022