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A199958
Decimal expansion of greatest x satisfying x^2 + 2*cos(x) = 4*sin(x).
3
2, 1, 1, 1, 5, 9, 4, 8, 6, 7, 3, 1, 3, 0, 9, 4, 1, 6, 6, 6, 4, 6, 4, 1, 3, 3, 1, 0, 9, 9, 2, 0, 7, 4, 5, 4, 6, 0, 6, 7, 6, 8, 3, 5, 7, 6, 1, 4, 3, 6, 4, 6, 4, 5, 3, 4, 0, 0, 6, 1, 8, 8, 8, 3, 7, 3, 2, 8, 4, 5, 1, 2, 2, 9, 1, 7, 9, 0, 0, 3, 6, 6, 6, 5, 8, 1, 5, 8, 8, 3, 6, 6, 7, 2, 6, 2, 4, 9, 1
OFFSET
1,1
COMMENTS
See A199949 for a guide to related sequences. The Mathematica program includes a graph.
LINKS
EXAMPLE
least x: 0.525416279282353649071522053392...
greatest x: 2.1115948673130941666464133109...
MATHEMATICA
a = 1; b = 2; c = 4;
f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
Plot[{f[x], g[x]}, {x, -1, 3}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, .52, .53}, WorkingPrecision -> 110]
RealDigits[r] (* A199957 *)
r = x /. FindRoot[f[x] == g[x], {x, 2.1, 2.2}, WorkingPrecision -> 110]
RealDigits[r] (* A199958 *)
PROG
(PARI) a=1; b=2; c=4; solve(x=0, 1, a*x^2 + b*cos(x) - c*sin(x)) \\ G. C. Greubel, Jun 22 2018
CROSSREFS
Cf. A199949.
Sequence in context: A292464 A090628 A054387 * A112734 A351699 A260685
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Nov 12 2011
STATUS
approved