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A199618
Decimal expansion of greatest x satisfying x^2+4*x*cos(x)=3*sin(x).
3
3, 4, 8, 2, 2, 6, 7, 6, 2, 4, 7, 8, 6, 1, 9, 3, 2, 0, 9, 0, 8, 6, 7, 0, 3, 6, 6, 7, 5, 5, 7, 6, 8, 0, 3, 7, 0, 7, 6, 2, 6, 9, 3, 1, 5, 6, 9, 4, 5, 6, 0, 3, 6, 9, 3, 8, 3, 9, 7, 6, 9, 9, 3, 4, 9, 0, 0, 4, 8, 4, 2, 1, 8, 7, 6, 3, 9, 8, 5, 1, 0, 8, 3, 9, 9, 3, 9, 4, 9, 6, 8, 6, 4, 8, 5, 8, 9, 5, 7
OFFSET
0,1
COMMENTS
See A199597 for a guide to related sequences. The Mathematica program includes a graph.
EXAMPLE
least: -0.5535433817860336287020344905911816930...
greatest: 3.4822676247861932090867036675576803...
MATHEMATICA
a = 1; b = 4; c = 3;
f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c*Sin[x]
Plot[{f[x], g[x]}, {x, -2, 4}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, -.56, -.55}, WorkingPrecision -> 110]
RealDigits[r] (* A199617, least of 4 roots *)
r = x /. FindRoot[f[x] == g[x], {x, 3.4, 3.5}, WorkingPrecision -> 110]
RealDigits[r] (* A199618, greatest of 4 roots *)
CROSSREFS
Cf. A199597.
Sequence in context: A016609 A376912 A346411 * A088745 A213922 A306568
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Nov 08 2011
STATUS
approved