A390699 Decimal expansion of cos(7*Pi/33).

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

Offset

0,1

Links

Table of n, a(n) for n=0..86.

Index entries for algebraic numbers, degree 10

Formula

Equals sin(19*Pi/66) = 2F1(-7/22,7/22;1/2;3/4) = -cos(26*Pi/33).

Third largest of the 10 real-valued roots of Product_{0<k<33 and k == 1 (mod 2) and gcd(k,33) = 1} 2*(cos(k*Pi/33) - x) = 1024*x^10 +512*x^9 -2560*x^8 -1280*x^7 +2176*x^6 +1088*x^5 -688*x^4 -344*x^3 +48*x^2 +24*x +1 =0.

Example

0.7860530947427874697567960561472203660398...

Mathematica

RealDigits[Cos[7Pi/33], 10, 87][[1]] (* James C. McMahon, Nov 25 2025 *)

Prog

(PARI) cos(7*Pi/33)

Crossrefs

cos(k*Pi/33) = 2F1(-k/22.k/22;1/2;3/4): A387450 (k = 1), A387440 (k = 3), A390698 (k = 5), this sequence (k = 7), 1/2 (k = 11), -1/2 (k = 22), -this (k = 26), -A390698 (k = 28), -A387440 (k = 30), -A387450 (k = 32).

Cf. A389480.

Sequence in context: A117239 A198365 A262898 * A004496 A197762 A181624

Adjacent sequences: A390696 A390697 A390698 * A390700 A390701 A390702

Keyword

nonn,cons

Author

A.H.M. Smeets, Nov 15 2025

Status

approved