A019815 Decimal expansion of sine of 6 degrees.
1, 0, 4, 5, 2, 8, 4, 6, 3, 2, 6, 7, 6, 5, 3, 4, 7, 1, 3, 9, 9, 8, 3, 4, 1, 5, 4, 8, 0, 2, 4, 9, 8, 1, 1, 9, 0, 8, 0, 6, 5, 5, 8, 6, 9, 4, 7, 4, 5, 9, 3, 1, 1, 3, 9, 9, 3, 2, 7, 5, 4, 7, 6, 7, 1, 2, 4, 8, 4, 6, 5, 0, 6, 9, 3, 1, 8, 0, 0, 4, 6, 8, 2, 8, 1, 8, 0, 3, 9, 8, 7, 9, 8, 6, 0, 4, 4, 2, 6
Offset: 0
Examples
sin(Pi/30) = 0.10452846...
Links
- Ivan Panchenko, Table of n, a(n) for n = 0..1000
- Wikipedia, Exact trigonometric constants
- Index entries for algebraic numbers, degree 4
Programs
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Mathematica
First[RealDigits[1/8 (-1 - Sqrt[5] + Sqrt[6 (5 - Sqrt[5])]), 10, 100]] (* Artur Jasinski, Oct 28 2008 *) RealDigits[Sin[6 Degree],10,120][[1]] (* Harvey P. Dale, Apr 27 2012 *)
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PARI
sin(Pi/30) \\ Charles R Greathouse IV, Jan 30 2016
Formula
Equals cos(7*Pi/15) = -cos(8*Pi/15) = 2F1(6/5,-1/5;1/2;3/4) / 2 = -2F1(13/10,-3/10;1/2;3/4) / 2. - R. J. Mathar, Oct 27 2008
Smallest positive of the 4 real-valued roots of 16*x^4+8*x^3-16*x^2-8*x+1=0. (Other A019887, -A019875, -A019851) - R. J. Mathar, Aug 31 2025
Comments