%I #9 Jul 09 2018 19:52:20
%S 1,1,0,8,8,1,1,8,8,2,9,7,1,7,2,7,6,2,1,8,5,8,4,9,5,3,5,2,2,8,5,8,9,1,
%T 7,2,5,5,4,0,0,8,9,9,4,0,1,9,4,8,5,0,6,8,1,9,7,6,4,9,9,3,1,5,7,1,7,8,
%U 4,8,7,1,3,8,8,5,5,5,9,5,8,9,9,7,8,4,3,9,2,3,8,0,5,3,6,3,5,7,8
%N Decimal expansion of greatest x satisfying 4*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="/A200304/b200304.txt">Table of n, a(n) for n = 1..10000</a>
%e least x: -0.4676436322290565342035400494771...
%e greatest x: 1.10881188297172762185849535228...
%t a = 4; 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, -1, 2}, {AxesOrigin -> {0, 0}}]
%t r = x /. FindRoot[f[x] == g[x], {x, -.47, -.46}, WorkingPrecision -> 110]
%t RealDigits[r] (* A200303 *)
%t r = x /. FindRoot[f[x] == g[x], {x, 1.1, 1.2}, WorkingPrecision -> 110]
%t RealDigits[r] (* A200304 *)
%o (PARI) a=4; b=-3; c=4; solve(x=1, 2, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jul 08 2018
%Y Cf. A199949.
%K nonn,cons
%O 1,4
%A _Clark Kimberling_, Nov 15 2011
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