A073052 Decimal expansion of cos(Pi/7).

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, 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, 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

Offset: 0

Author

Robert G. Wilson v, Aug 15 2002

Keywords

• cons
• nonn

Comments

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

Examples

			Cos(Pi/7) = 0.90096886790241912623610231950744505116139...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..10000
• Kevin S. Brown's MathPages, Radical Expression For cos(2*Pi/7)
• Index entries for algebraic numbers, degree 3.

Crossrefs

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

Programs

Magma

R:= RealField(120); Cos(Pi(R)/7); // G. C. Greubel, Sep 04 2022

Mathematica

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

PARI

cos(Pi/7) \\ Charles R Greathouse IV, May 13 2019

SageMath

numerical_approx(cos(pi/7), digits=120) # G. C. Greubel, Sep 04 2022

Formula

Equals Hypergeometric2F1([5/7, 2/7], [1/2], 3/4)/2 . - R. J. Mathar, Oct 27 2008

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