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).
Paul J. Nahin, Inside interesting integrals, Undergrad. Lecture Notes in Physics, Springer (2020), chapter 1.5
Simon Plouffe, sin(1)
Eric Weisstein's World of Mathematics, Factorial Sums
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
Equals Integral_{x=-1..1} cos(x)/[exp(1/x)+1] dx. [Nahin]. - R. J. Mathar, May 16 2024
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
KEYWORD
AUTHOR
Albert du Toit (dutwa(AT)intekom.co.za), N. J. A. Sloane
STATUS
approved