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%I #8 Jun 25 2018 22:54:25
%S 1,0,5,6,6,9,8,3,7,6,9,4,2,8,7,8,1,2,2,1,9,2,4,0,8,3,0,3,1,1,7,5,2,5,
%T 0,9,3,5,5,7,1,3,6,8,6,5,0,9,1,9,3,5,0,7,4,4,3,8,6,6,4,9,4,2,8,0,6,9,
%U 8,4,2,7,3,3,0,3,3,7,1,5,8,8,7,0,0,9,2,6,3,1,0,0,5,0,4,1,4,2,9
%N Decimal expansion of greatest x satisfying 2*x^2 - 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="/A200110/b200110.txt">Table of n, a(n) for n = 1..10000</a>
%e least x: -0.35236500577732645310286619535999...
%e greatest x: 1.0566983769428781221924083031175250...
%t a = 2; b = -1; c = 2;
%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, -.36, -.35}, WorkingPrecision -> 110]
%t RealDigits[r] (* A200109 *)
%t r = x /. FindRoot[f[x] == g[x], {x, 1.05, 1.06}, WorkingPrecision -> 110]
%t RealDigits[r] (* A200110 *)
%o (PARI) a=2; b=-1; c=2; solve(x=1, 2, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jun 25 2018
%Y Cf. A199949.
%K nonn,cons
%O 1,3
%A _Clark Kimberling_, Nov 13 2011
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