A019987 Decimal expansion of tangent of 89 degrees.

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

Offset

2,1

Comments

Also cotangent of 1 degree. - Mohammad K. Azarian, Jan 21 2006

An algebraic integer of degree 24. - Charles R Greathouse IV, Aug 27 2017

The least k > 0 such that floor(cot(1°)*10^k) is prime is k = 39. - M. F. Hasler, May 19 2023

Links

Ivan Panchenko, Table of n, a(n) for n = 2..1000.

Art of Problem Solving, USAMO 1996, Problem 1.

Mohammad K. Azarian, Forty-Five Nested Equilateral Triangles and cosecant of 1 degree, Problem 813, College Mathematics Journal, Vol. 36, No. 5, November 2005, p. 413-414; Solution, College Mathematics Journal, Vol. 37, No. 5, November 2006, pp. 394-395.

User ssaamil, I found a cool number I'd like to share, 57289961630759424687278147537112577980217. In reddit.com/r/math, May 12 2023

Index to sequences related to Olympiads.

Index entries for algebraic numbers, degree 24

Formula

Equals (Sum_{k=1..90} 2*k*sin(2*k)) / 90, with k in degrees (link USAMO 1996). - Bernard Schott, Apr 30 2022

A largest of the 24 real-valued roots of 1 -48*x +x^24 -564*x^22 +21186*x^20 -269412*x^18 +1470447*x^16 -3923304*x^14 +5407388*x^12 -3923304*x^10 +1470447*x^8- 269412*x^6 +21186*x^4 -564*x^2 -48*x^23 +1456*x^21 -12432*x^19 +17424*x^17 +45344*x^15 -51744*x^13 -51744*x^11 +45344*x^9 +17424*x^7 -12432*x^5 +1456*x^3 =0.- R. J. Mathar, Aug 29 2025

Example

57.28996...

Maple

evalf(cot(Pi/180), 100); # Bernard Schott, Apr 30 2022

Mathematica

First[RealDigits[Cot[Pi/180], 10, 100]] (* Paolo Xausa, Apr 23 2024 *)

Prog

(PARI) tan(89*Pi/180) \\ Charles R Greathouse IV, Aug 27 2017

Crossrefs

Cf. A073449, A019899-A019986 (same for 1, ..., 88 degrees).

Sequence in context: A153110 A099283 A368663 * A072097 A259070 A110937

Adjacent sequences: A019984 A019985 A019986 * A019988 A019989 A019990

Keyword

nonn,cons

Author

N. J. A. Sloane

Extensions

Edited by N. J. A. Sloane, Aug 19 2008 at the suggestion of R. J. Mathar

Status

approved