A049470 Decimal expansion of cos(1).

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

Offset

0,1

Comments

Also, decimal expansion of the real part of e^i. - Bruno Berselli, Feb 08 2013

By the Lindemann-Weierstrass theorem, this constant is transcendental. - Charles R Greathouse IV, May 13 2019

Links

Muniru A Asiru, Table of n, a(n) for n = 0..2000

Mohammad K. Azarian, Forty-Five Nested Equilateral Triangles and cosecant of 1 degree, Problem 813, College Mathematics Journal, Vol. 36, No. 5, November 2005, p. 413-414.

Mohammad K. Azarian, Solution of Forty-Five Nested Equilateral Triangles and cosecant of 1 degree, Problem 813, College Mathematics Journal, Vol. 37, No. 5, November 2006, pp. 394-395.

I. S. Gradsteyn, I. M. Ryzhik, Table of integrals, series and products, (1980), page 10 (formula 0.245.7).

Simon Plouffe, cos(1)

Eric Weisstein's World of Mathematics, Factorial Sums

Index entries for transcendental numbers

Formula

Continued fraction representation: cos(1) = 1/(1 + 1/(1 + 2/(11 + 12/(29 + ... + (2*n - 2)*(2*n - 3)/((4*n^2 - 2*n - 1) + ... ))))). See A275651 for proof. Cf. A073743. - Peter Bala, Sep 02 2016

Equals Sum_{k >= 0} (-1)^k/A010050(k), where A010050(k) = (2k)! [See Gradshteyn and Ryzhik]. - A.H.M. Smeets, Sep 22 2018

Equals 1/A073448. - Alois P. Heinz, Jan 23 2023

Example

0.5403023058681397...

Maple

evalf(cos(1)); # Altug Alkan, Sep 22 2018

Mathematica

RealDigits[Cos[1], 10, 110] [[1]]

Prog

(PARI) cos(1) \\ Charles R Greathouse IV, Jan 04 2016

Crossrefs

Cf. A049469 (imaginary part of e^i), A211883 (real part of -(i^e)), A211884 (imaginary part of -(i^e)). - Bruno Berselli, Feb 08 2013

Cf. A073743 ( cosh(1) ), A073448, A275651.

Cf. A068985, A346441, A346440, A346439, A346438, A346437, A346436, A346435, A196498.

Sequence in context: A159799 A185579 A197134 * A309699 A153106 A021189

Adjacent sequences: A049467 A049468 A049469 * A049471 A049472 A049473

Keyword

cons,easy,nonn

Author

Albert du Toit (dutwa(AT)intekom.co.za), N. J. A. Sloane

Status

approved