A019973 Decimal expansion of tangent of 75 degrees.
3, 7, 3, 2, 0, 5, 0, 8, 0, 7, 5, 6, 8, 8, 7, 7, 2, 9, 3, 5, 2, 7, 4, 4, 6, 3, 4, 1, 5, 0, 5, 8, 7, 2, 3, 6, 6, 9, 4, 2, 8, 0, 5, 2, 5, 3, 8, 1, 0, 3, 8, 0, 6, 2, 8, 0, 5, 5, 8, 0, 6, 9, 7, 9, 4, 5, 1, 9, 3, 3, 0, 1, 6, 9, 0, 8, 8, 0, 0, 0, 3, 7, 0, 8, 1, 1, 4, 6, 1, 8, 6, 7, 5, 7, 2, 4, 8, 5, 7
Offset: 1
Examples
3.732050807568877293527446341505872366942805253810380628...
Links
- G. C. Greubel, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Ivan Panchenko)
- Wikipedia, Exact trigonometric constants.
- Index entries for algebraic numbers, degree 2.
Programs
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Magma
SetDefaultRealField(RealField(100)); 2 + Sqrt(3); // G. C. Greubel, Nov 20 2018
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Mathematica
RealDigits[Tan[75 Degree],10,120][[1]] (* Harvey P. Dale, Nov 08 2011 *) RealDigits[2+Sqrt[3], 10, 100][[1]] (* G. C. Greubel, Nov 20 2018 *)
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PARI
sqrt(3)+2 \\ Charles R Greathouse IV, Oct 17 2016
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Sage
numerical_approx(2+sqrt(3), digits=100) # G. C. Greubel, Nov 20 2018
Formula
Equals 2 + sqrt(3) = 2+A002194 = cotangent of 15 degrees. - Rick L. Shepherd, Jul 04 2004
Equals exp(arccosh(2)). - Amiram Eldar, Aug 07 2023
c^n = A001835(n) + (1 + sqrt(3)) * A001353(n) = A001075(n) + sqrt(3) * A001353(n); where c = 2 + sqrt(3). - Gary W. Adamson, Oct 14 2023
Equals lim_{n->oo} S(n, 4)/ S(n-1, 4), with the S-Chebyshev polynomial (see A049310) S(n, 4) = A001353(n+1). See the A001353 formula from Oct 06 2002 by Gregory V. Richardson. - Wolfdieter Lang, Nov 15 2023
Equals 1/A019913. - Hugo Pfoertner, Mar 24 2024
Extensions
Checked by Neven Juric (neven.juric(AT)apis-it.hr), Feb 04 2008
Comments