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%I #8 Jul 01 2018 08:34:51
%S 1,1,6,4,7,2,0,1,3,2,6,0,0,0,8,6,5,4,8,1,4,4,1,7,3,6,0,3,9,1,7,6,2,9,
%T 3,4,2,8,3,8,8,5,9,8,2,9,2,3,6,1,6,8,4,5,0,1,3,9,9,2,3,7,8,1,6,7,5,4,
%U 2,8,8,0,2,7,2,0,0,6,5,0,9,7,8,3,9,7,1,5,4,7,9,2,5,5,4,8,9,5,0
%N Decimal expansion of greatest x satisfying 3*x^2 - 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="/A200228/b200228.txt">Table of n, a(n) for n = 1..10000</a>
%e least x: -0.21220726159791829897823740501037540...
%e greatest x: 1.164720132600086548144173603917629...
%t a = 3; b = -1; 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, -.22, -.21}, WorkingPrecision -> 110]
%t RealDigits[r] (* A200227 *)
%t r = x /. FindRoot[f[x] == g[x], {x, 1.1, 1.2}, WorkingPrecision -> 110]
%t RealDigits[r] (* A200228 *)
%o (PARI) a=3; b=-1; c=4; solve(x=1, 2, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jun 30 2018
%Y Cf. A199949.
%K nonn,cons
%O 1,3
%A _Clark Kimberling_, Nov 14 2011
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