A232736 Decimal expansion of sin(Pi/14), or the imaginary part of (-1)^(1/7).

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

Offset: 0

Author

Stanislav Sykora, Nov 29 2013

Keywords

• nonn
• cons
• easy
• changed

Comments

The corresponding real part is in A232735.

Root of the equation 1 - 4*x - 4*x^2 + 8*x^3 = 0. - Vaclav Kotesovec, Apr 04 2021

The other 2 roots are -A362922 and A073052. - R. J. Mathar, Aug 29 2025

Examples

			0.222520933956314404288902564496794759466355568764544955311987...
		

Links

• Stanislav Sykora, Table of n, a(n) for n = 0..1000
• Index entries for algebraic numbers, degree 3.

Crossrefs

Cf. A232735 (real part), A010503 (imag(I^(1/2))), A182168 (imag(I^(1/4))), A019827 (imag(I^(1/5))), A019824 (imag(I^(1/6))), A232738 (imag(I^(1/8))), A019819 (imag(I^(1/9))), A019818 (imag(I^(1/10))).

See also A323601.

Programs

Magma

R:= RealField(120); Cos(3*Pi(R)/7); // G. C. Greubel, Sep 04 2022

Mathematica

RealDigits[Cos[3*Pi/7], 10, 120][[1]] (* G. C. Greubel, Sep 04 2022 *)

PARI

sin(Pi/14) \\ Charles R Greathouse IV, Feb 04 2025

PARI

polrootsreal(8*x^3-4*x^2-4*x+1)[2] \\ Charles R Greathouse IV, Feb 04 2025

SageMath

numerical_approx(cos(3*pi/7), digits=120) # G. C. Greubel, Sep 04 2022

Formula

Equals cos(3*Pi/7). - G. C. Greubel, Sep 04 2022

Equals 4*A073052^3 -3*A073052. - R. J. Mathar, Aug 29 2025

This^2 + A232735^2 = 1. - R. J. Mathar, Aug 31 2025