

A049469


Decimal expansion of sin(1).


41



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
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OFFSET

0,1


COMMENTS

Also, decimal expansion of the imaginary part of e^i.  Bruno Berselli, Feb 08 2013
By the LindemannWeierstrass 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, FortyFive Nested Equilateral Triangles and cosecant of 1 degree, Problem 813, College Mathematics Journal, Vol. 36, No. 5, November 2005, p. 413414.
Mohammad K. Azarian, Solution of FortyFive Nested Equilateral Triangles and cosecant of 1 degree, Problem 813, College Mathematics Journal, Vol. 37, No. 5, November 2006, pp. 394395.
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)^(k1)/((2k1)!) = Sum_{k > 0} (1)^(k1)/A009445(k1) [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: A247036 A202320 A011267 * A021547 A154527 A145435
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



