A019864 -id:A019864 - cp's OEIS frontend

A019879 Decimal expansion of sine of 70 degrees.

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

Offset: 0

N. J. A. Sloane

It is well known that the length sin 70° (cos 20°) is not constructible with ruler and compass, since it is a root of the irreducible polynomial 8x^3 - 6x - 1 and 3 fails to divide any power of 2. - Jean-François Alcover, Aug 10 2014 [cf. the Maxfield ref.]
A cubic number with denominator 2. - Charles R Greathouse IV, Aug 27 2017
From Peter Bala, Oct 21 2021: (Start)
The minimal polynomial of cos(Pi/9) is 8*x^3 - 6*x - 1 with discriminant (2^6)*(3^4), a square: hence the Galois group of the algebraic number field Q(sin(70°) over Q is the cyclic group of order 3.
The two other zeros of the minimal polynomial are cos(5*Pi/9) = - A019819 and cos(7*Pi/9) = - A019859. The mapping z -> 1 - 2*z^2 cyclically permutes the three zeros.  The inverse permutation is given by the mapping z -> 2*z^2 - z - 1. (End)

			0.93969262...

J. E. Maxfield and M. W. Maxfield, Abstract Algebra and Solution by Radicals, Dover Publications ISBN 0-486-67121-6, (1992), p. 197.

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Michael Penn, Proof that cos(20°) is irrational, YouTube video, 2022.
Index entries for algebraic numbers, degree 3

Cf. A019819, A019844, A019859, A214778, A332437.

RealDigits[Sin[70 Degree],10,120][[1]] (* Harvey P. Dale, Aug 17 2012 *)

cos(Pi/9) \\ Charles R Greathouse IV, Aug 27 2017

Equals 2*A019844*A019864. - R. J. Mathar, Jan 17 2021
Equals cos(Pi/9) = (1/2)*A332437. - Peter Bala, Oct 21 2021
Equals 2F1(-1/6,1/6 ; 1/2; 3/4). - R. J. Mathar, Aug 31 2025

A019953 Decimal expansion of tangent of 55 degrees.

Original entry on oeis.org

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

Offset: 1

N. J. A. Sloane

Also the decimal expansion of cotangent of 35 degrees. - Ivan Panchenko, Sep 01 2014

			1.4281480067421145021606184849985007396338016120753190976117941...

Ivan Panchenko, Table of n, a(n) for n = 1..1000

Cf. A019864 (sine of 55 degrees).

SetDefaultRealField(RealField(100)); R:= RealField(); Tan(11*Pi(R)/36); // G. C. Greubel, Nov 22 2018

RealDigits[Tan[11*Pi/36], 10, 100][[1]] (* G. C. Greubel, Nov 22 2018 *)

default(realprecision, 100); tan(11*Pi/36) \\ G. C. Greubel, Nov 22 2018

numerical_approx(tan(11*pi/36), digits=100) # G. C. Greubel, Nov 22 2018

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A019879 Decimal expansion of sine of 70 degrees.

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