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A200296 Decimal expansion of greatest x satisfying 4*x^2 - 2*cos(x) = 3*sin(x).

%I A200296 #12 Feb 12 2025 14:35:09
%S A200296 9,4,9,1,4,5,7,1,9,4,2,3,0,0,9,8,4,4,8,1,8,9,1,9,6,7,0,8,5,7,2,5,6,6,
%T A200296 1,0,8,7,9,0,6,6,3,3,3,0,0,2,9,8,9,2,3,1,7,5,6,2,8,7,1,6,4,0,4,2,2,9,
%U A200296 8,6,6,4,6,6,4,9,9,0,2,8,0,0,7,2,8,4,5,1,8,0,1,9,4,7,2,4,3,7,8
%N A200296 Decimal expansion of greatest x satisfying 4*x^2 - 2*cos(x) = 3*sin(x).
%C A200296 See A199949 for a guide to related sequences. The Mathematica program includes a graph.
%H A200296 G. C. Greubel, <a href="/A200296/b200296.txt">Table of n, a(n) for n = 0..10000</a>
%H A200296 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A200296 least x: -0.40500714967330681353010125636730...
%e A200296 greatest x: 0.949145719423009844818919670857...
%t A200296 a = 4; b = -2; c = 3;
%t A200296 f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
%t A200296 Plot[{f[x], g[x]}, {x, -1, 1}, {AxesOrigin -> {0, 0}}]
%t A200296 r = x /. FindRoot[f[x] == g[x], {x, -.41, -.40}, WorkingPrecision -> 110]
%t A200296 RealDigits[r]   (* A200295 *)
%t A200296 r = x /. FindRoot[f[x] == g[x], {x, .94, .95}, WorkingPrecision -> 110]
%t A200296 RealDigits[r]   (* A200296 *)
%o A200296 (PARI) a=4; b=-2; c=3; solve(x=0, 1, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jul 08 2018
%Y A200296 Cf. A199949.
%K A200296 nonn,cons
%O A200296 0,1
%A A200296 _Clark Kimberling_, Nov 15 2011