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A019970 Decimal expansion of tangent of 72 degrees.

%I A019970 #60 Aug 31 2025 13:02:00
%S A019970 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,
%T A019970 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,
%U A019970 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
%N A019970 Decimal expansion of tangent of 72 degrees.
%C A019970 Also the decimal expansion of cotangent of 18 degrees. - _Mohammad K. Azarian_, Jun 30 2013
%C A019970 A quartic integer. - _Charles R Greathouse IV_, Aug 27 2017
%C A019970 Length of the second longest diagonal in a regular 10-gon with unit side. - _Mohammed Yaseen_, Nov 12 2020
%H A019970 Ivan Panchenko, <a href="/A019970/b019970.txt">Table of n, a(n) for n = 1..1000</a>
%H A019970 Wikipedia, <a href="http://en.wikipedia.org/wiki/Exact_trigonometric_constants">Exact trigonometric constants</a>.
%H A019970 <a href="/index/Al#algebraic_04">Index entries for algebraic numbers, degree 4</a>
%F A019970 Equals sqrt(5 + 2*sqrt(5)). - _R. J. Mathar_, Jun 18 2006
%F A019970 Equals tan(66 degrees) + tan(36 degrees) + tan(6 degrees). - _Amiram Eldar_, Apr 07 2022
%F A019970 Largest positive of the 4 real-valued roots of x^4-10*x^2+5=0. - _R. J. Mathar_, Aug 31 2025
%e A019970 tan(2*Pi/5) = 3.077683537175253402570290576036909824006702143537792427...
%t A019970 RealDigits[Tan[72 Degree],10,120][[1]] (* _Harvey P. Dale_, Apr 30 2012 *)
%t A019970 RealDigits[Sqrt[5 + 2*Sqrt[5]], 10, 100][[1]] (* _G. C. Greubel_, Nov 21 2018 *)
%o A019970 (PARI) tan(2*Pi/5) \\ _Charles R Greathouse IV_, Aug 27 2017
%o A019970 (Magma) SetDefaultRealField(RealField(100)); Sqrt(5+2*Sqrt(5)); // _G. C. Greubel_, Nov 21 2018
%o A019970 (Sage) numerical_approx(tan(2*pi/5), digits=100) # _G. C. Greubel_, Nov 21 2018
%Y A019970 Cf. A019881 (sine of 72 degrees).
%Y A019970 Cf. A019904, A019934, A019964.
%K A019970 nonn,cons,changed
%O A019970 1,1
%A A019970 _N. J. A. Sloane_