cp's OEIS Frontend

A019946 Decimal expansion of tangent of 48 degrees.

%I A019946 #31 Sep 06 2025 08:09:07
%S A019946 1,1,1,0,6,1,2,5,1,4,8,2,9,1,9,2,8,7,0,1,4,3,4,8,1,9,6,4,1,6,5,1,3,5,
%T A019946 5,3,2,5,7,6,9,5,9,5,1,0,3,9,0,8,5,9,0,4,8,1,8,4,4,0,2,2,2,0,2,8,9,9,
%U A019946 6,5,5,3,5,8,7,3,7,3,1,3,6,5,4,5,8,5,0,6,1,6,9,2,1,5,8,7,8,6,8
%N A019946 Decimal expansion of tangent of 48 degrees.
%C A019946 Also the decimal expansion of cotangent of 42 degrees. - _Ivan Panchenko_, Sep 01 2014
%H A019946 Ivan Panchenko, <a href="/A019946/b019946.txt">Table of n, a(n) for n = 1..1000</a>
%H A019946 Wikipedia, <a href="http://en.wikipedia.org/wiki/Exact_trigonometric_constants">Exact trigonometric constants</a>
%H A019946 <a href="/index/Al#algebraic_08">Index entries for algebraic numbers, degree 8</a>
%F A019946 Equals cot(7*Pi/30) = sqrt(23 - 10*sqrt(5) + 2*sqrt(3*(85 -38*sqrt(5)))). - _G. C. Greubel_, Nov 24 2018
%F A019946 Let r(n) = (n - 1)/(n + 1) if n mod 4 = 1, (n + 1)/(n - 1) otherwise; then this constant equals with Product_{n>=0} r(30*n+15) = (8/7) * (22/23) * (38/37) * (52/53) ... - _Dimitris Valianatos_, Sep 14 2019
%F A019946 Equals A019857 / A019851. - _R. J. Mathar_, Sep 06 2025
%e A019946 tan(4*Pi/15) = 1.11061251482919287014348196416513553257695951039085904818440222...
%t A019946 RealDigits[Tan[48 Degree],10,120][[1]] (* _Harvey P. Dale_, Nov 26 2011 *)
%t A019946 RealDigits[Tan[4*Pi/15], 10, 100][[1]] (* _G. C. Greubel_, Nov 24 2018 *)
%o A019946 (PARI) default(realprecision, 100); tan(4*Pi/15) \\ _G. C. Greubel_, Nov 24 2018
%o A019946 (Magma) SetDefaultRealField(RealField(100)); R:= RealField(); Tan(4*Pi(R)/15); // _G. C. Greubel_, Nov 24 2018
%o A019946 (Sage) numerical_approx(tan(4*pi/15), digits=100) # _G. C. Greubel_, Nov 24 2018
%Y A019946 Cf. A019857 (sine of 48 degrees).
%K A019946 nonn,cons,changed
%O A019946 1,5
%A A019946 _N. J. A. Sloane_