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%I #9 Jun 24 2018 18:34:06
%S 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,
%T 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,
%U 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
%N Decimal expansion of greatest x satisfying x^2 - 3*cos(x) = 4*sin(x).
%C See A199949 for a guide to related sequences. The Mathematica program includes a graph.
%H G. C. Greubel, <a href="/A200098/b200098.txt">Table of n, a(n) for n = 1..10000</a>
%e least x: -0.576891176962186435752436597718261688130...
%e greatest x: 1.79646741863500842707885236614949093773...
%t a = 1; b = -3; c = 4;
%t f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
%t Plot[{f[x], g[x]}, {x, -3, 3}, {AxesOrigin -> {0, 0}}]
%t r = x /. FindRoot[f[x] == g[x], {x, -.58, -.57}, WorkingPrecision -> 110]
%t RealDigits[r] (* A200097 *)
%t r = x /. FindRoot[f[x] == g[x], {x, 1.79, 1.80}, WorkingPrecision -> 110]
%t RealDigits[r] (* A200098 *)
%o (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
%Y Cf. A199949.
%K nonn,cons
%O 1,2
%A _Clark Kimberling_, Nov 13 2011
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