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

0,1

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

Other roots of the polynomial: A232736, -A362922. - R. J. Mathar, Sep 06 2025

The 7th cyclotomic polynomial is 1+x+x^2+x^3+..+x^6 and has roots -this +- A323601*i, -A232736 +- A232735*i, A362922 +- 0.78183148..*i. - R. J. Mathar, Jun 11 2026

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.

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

Example

Cos(Pi/7) = sin(5*Pi/14) = 0.90096886790241912623610231950744505116139...

Mathematica

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

Prog

(PARI) cos(Pi/7) \\ Charles R Greathouse IV, May 13 2019
(Magma) R:= RealField(120); Cos(Pi(R)/7); // G. C. Greubel, Sep 04 2022
(SageMath) numerical_approx(cos(pi/7), digits=120) # G. C. Greubel, Sep 04 2022

Crossrefs

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

Sequence in context: A199870 A132267 A021115 * A230068 A176908 A005083

Adjacent sequences: A073049 A073050 A073051 * A073053 A073054 A073055

Keyword

cons,nonn

Author

Robert G. Wilson v, Aug 15 2002

Status

approved