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A200098
Decimal expansion of greatest x satisfying x^2 - 3*cos(x) = 4*sin(x).
3
1, 7, 9, 6, 4, 6, 7, 4, 1, 8, 6, 3, 5, 0, 0, 8, 4, 2, 7, 0, 7, 8, 8, 5, 2, 3, 6, 6, 1, 4, 9, 4, 9, 0, 9, 3, 7, 7, 3, 8, 6, 0, 8, 3, 6, 2, 1, 3, 7, 1, 9, 9, 8, 4, 1, 8, 1, 9, 2, 1, 5, 3, 1, 6, 9, 4, 3, 4, 1, 7, 4, 7, 5, 9, 0, 5, 3, 9, 8, 9, 7, 9, 9, 3, 1, 0, 0, 7, 7, 3, 9, 4, 9, 0, 9, 4, 3, 3, 5
OFFSET
1,2
COMMENTS
See A199949 for a guide to related sequences. The Mathematica program includes a graph.
LINKS
EXAMPLE
least x: -0.576891176962186435752436597718261688130...
greatest x: 1.79646741863500842707885236614949093773...
MATHEMATICA
a = 1; b = -3; c = 4;
f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
Plot[{f[x], g[x]}, {x, -3, 3}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, -.58, -.57}, WorkingPrecision -> 110]
RealDigits[r] (* A200097 *)
r = x /. FindRoot[f[x] == g[x], {x, 1.79, 1.80}, WorkingPrecision -> 110]
RealDigits[r] (* A200098 *)
PROG
(PARI) a=1; b=-3; c=4; solve(x=1, 2, a*x^2 + b*cos(x) - c*sin(x)) \\ G. C. Greubel, Jun 24 2018
CROSSREFS
Cf. A199949.
Sequence in context: A099877 A197327 A199471 * A239069 A154168 A019644
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Nov 13 2011
STATUS
approved