A049469 Decimal expansion of sin(1).

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

Offset

0,1

Comments

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

By the Lindemann-Weierstrass theorem, this constant is transcendental. - Charles R Greathouse IV, May 12 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 0.245.8).

Simon Plouffe, sin(1)

Eric Weisstein's World of Mathematics, Factorial Sums

Index entries for transcendental numbers

Formula

Continued fraction representation: sin(1) = 1 - 1/(6 + 6/(19 + 20/(41 + ... + (2*n - 1)*(2*n - 2)/((4*n^2 + 2*n - 1) + ... )))). See A074790 for details. - Peter Bala, Jan 30 2015

Equals Sum_{k > 0} (-1)^(k-1)/((2k-1)!) = Sum_{k > 0} (-1)^(k-1)/A009445(k-1) [See Gradshteyn and Ryzhik]. - A.H.M. Smeets, Sep 22 2018

Equals Product{k>=1} cos(1/2^k). - Amiram Eldar, Aug 20 2020

Example

0.8414709848078965...

Maple

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

Mathematica

RealDigits[N[Sin[1], 110]] [[1]]

Prog

(PARI) sin(1) \\ Charles R Greathouse IV, Aug 20 2012
(PARI) sumalt(n=0, (-1)^(n%2)/(2*n+1)!) \\ Gheorghe Coserea, Sep 23 2018

Crossrefs

Cf. A049470 (real part of e^i), A211883 (real part of -(i^e)), A211884 (imaginary part of -(i^e)). - Bruno Berselli, Feb 08 2013

Cf. A074790.

Sequence in context: A371861 A202320 A011267 * A349625 A343739 A021547

Adjacent sequences: A049466 A049467 A049468 * A049470 A049471 A049472

Keyword

cons,easy,nonn

Author

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

Status

approved