A019987 - OEIS

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

(list; constant; graph; refs; listen; history; text; internal format)

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

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