%I #9 Jun 22 2018 07:58:22
%S 5,8,8,4,7,0,8,6,9,2,8,6,8,5,2,6,1,6,4,9,9,7,9,8,6,4,8,5,6,0,3,6,6,1,
%T 8,8,2,9,8,3,2,9,5,4,3,1,0,7,1,1,9,3,6,5,0,0,9,1,7,5,7,7,4,4,8,9,7,9,
%U 1,0,8,7,6,1,0,5,0,6,5,4,1,1,8,9,1,8,1,9,7,5,0,0,7,4,4,7,5,3,6
%N Decimal expansion of least x satisfying 4*x^2-3*cos(x)=2*sin(x).
%C See A199949 for a guide to related sequences. The Mathematica program includes a graph.
%H G. C. Greubel, <a href="/A200297/b200297.txt">Table of n, a(n) for n = 0..10000</a>
%e least x: -0.58847086928685261649979864856036...
%e greatest x: 0.922697336548314794603906551791...
%t a = 4; b = -3; c = 2;
%t f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
%t Plot[{f[x], g[x]}, {x, -1, 1}, {AxesOrigin -> {0, 0}}]
%t r = x /. FindRoot[f[x] == g[x], {x, -.59, -.58}, WorkingPrecision -> 110]
%t RealDigits[r] (* A200297 *)
%t r = x /. FindRoot[f[x] == g[x], {x, .92, .93}, WorkingPrecision -> 110]
%t RealDigits[r] (* A200298 *)
%o (PARI) a=4; b=-3; c=2; solve(x=-.59, -.58, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jun 22 2018
%Y Cf. A199949.
%K nonn,cons
%O 0,1
%A _Clark Kimberling_, Nov 15 2011
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