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A197476
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Decimal expansion of least x>0 having cos(x) = cos(2*x)^2.
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53
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1, 1, 3, 7, 7, 4, 3, 9, 3, 2, 9, 0, 5, 4, 5, 5, 5, 5, 7, 7, 8, 9, 4, 4, 9, 8, 6, 0, 0, 5, 5, 0, 0, 8, 3, 4, 9, 5, 8, 4, 8, 0, 4, 2, 9, 0, 3, 4, 9, 5, 7, 5, 2, 7, 2, 0, 1, 5, 1, 8, 2, 5, 2, 6, 7, 3, 6, 0, 9, 8, 3, 4, 7, 3, 4, 7, 2, 7, 2, 1, 7, 7, 9, 8, 8, 0, 3, 2, 8, 0, 5, 1, 7, 6, 4, 4, 7, 2, 7
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OFFSET
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1,3
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COMMENTS
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The Mathematica program includes a graph. Guide for least x>0 satisfying cos(b*x) = cos(c*x)^2, for selected b and c:
b.....c......x
4.....1.......A168229, arctan(sqrt(7))
6.....3.......A019670, Pi/3, tangency point
Pi/2..Pi/6....3
See A197133 for a guide for least x>0 satisfying sin(b*x) = sin(c*x)^2 for selected b and c.
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LINKS
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EXAMPLE
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1.137743932905455557789449860055008349584...
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MATHEMATICA
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b = 1; c = 2; f[x_] := Cos[x]
t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, 1.1, 1.3}, WorkingPrecision -> 200]
Plot[{f[b*x], f[c*x]^2}, {x, 0, 2}]
(* or *)
RealDigits[ ArcCos[ ((19 - 3*Sqrt[33])^(1/3) + (19 + 3*Sqrt[33])^(1/3) - 2)/6], 10, 99] // First (* Jean-François Alcover, Feb 19 2013 *)
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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