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%I #9 Jun 24 2018 18:32:45
%S 1,4,9,2,6,6,5,9,2,3,5,2,5,1,3,2,2,0,6,9,6,9,2,4,3,0,5,9,8,3,4,9,3,6,
%T 8,6,1,2,4,0,4,8,8,9,5,6,1,6,3,5,6,4,3,2,6,8,3,4,4,8,4,7,9,6,0,6,9,1,
%U 2,4,2,5,9,1,7,2,9,7,0,3,5,3,3,6,8,4,1,3,1,4,1,0,3,0,8,7,9,1,2
%N Decimal expansion of greatest x satisfying 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="/A200094/b200094.txt">Table of n, a(n) for n = 1..10000</a>
%e least x: -0.8029921542978842507203354534748712742...
%e greatest x: 1.492665923525132206969243059834936861...
%t a = 1; 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, -2, 2}, {AxesOrigin -> {0, 0}}]
%t r = x /. FindRoot[f[x] == g[x], {x, -.81, -.80}, WorkingPrecision -> 110]
%t RealDigits[r] (* A200093 *)
%t r = x /. FindRoot[f[x] == g[x], {x, 1.49, 1.50}, WorkingPrecision -> 110]
%t RealDigits[r] (* A200094 *)
%o (PARI) a=1; b=-3; c=2; 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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