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
Examples
0.8414709848078965...
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
- Index entries for transcendental numbers
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.
Programs
-
Maple
evalf(sin(1)); # Altug Alkan, Sep 22 2018
-
Mathematica
RealDigits[N[Sin[1], 110]] [[1]]
-
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
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
Comments