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Decimal expansion of cos(Pi/7).
8

%I #14 Feb 05 2025 11:42:58

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

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

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

%N Decimal expansion of cos(Pi/7).

%C Cubic number with denominator 2 and minimal polynomial 8*x^3 - 4*x^2 - 4*x + 1. - _Charles R Greathouse IV_, May 13 2019

%H G. C. Greubel, <a href="/A073052/b073052.txt">Table of n, a(n) for n = 0..10000</a>

%H Kevin S. Brown's MathPages, <a href="http://www.mathpages.com/home/kmath186.htm">Radical Expression For cos(2*Pi/7)</a>

%H <a href="/index/Al#algebraic_03">Index entries for algebraic numbers, degree 3</a>.

%F Equals Hypergeometric2F1([5/7, 2/7], [1/2], 3/4)/2 . - _R. J. Mathar_, Oct 27 2008

%F Equals (1/6)*(1 + (7*(-1 +3*sqrt(3)*I)/2)^(1/3) + (-7*(1 +3*sqrt(3)*I)/2)^(1/3)). - _G. C. Greubel_, Sep 04 2022

%e Cos(Pi/7) = 0.90096886790241912623610231950744505116139...

%t RealDigits[ Cos[Pi/7], 10, 105] [[1]]

%o (PARI) cos(Pi/7) \\ _Charles R Greathouse IV_, May 13 2019

%o (Magma) R:= RealField(120); Cos(Pi(R)/7); // _G. C. Greubel_, Sep 04 2022

%o (SageMath) numerical_approx(cos(pi/7), digits=120) # _G. C. Greubel_, Sep 04 2022

%Y Cf. A232736 (cos(3*Pi/7)).

%K cons,nonn,changed

%O 0,1

%A _Robert G. Wilson v_, Aug 15 2002