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A200298 Decimal expansion of greatest x satisfying 4*x^2-3*cos(x)=2*sin(x).

%I A200298 #12 Feb 12 2025 14:36:12
%S A200298 9,2,2,6,9,7,3,3,6,5,4,8,3,1,4,7,9,4,6,0,3,9,0,6,5,5,1,7,9,1,5,6,2,3,
%T A200298 6,8,8,9,4,9,0,9,0,4,9,0,7,7,2,5,7,0,5,8,6,7,3,2,2,9,0,3,3,1,1,2,1,4,
%U A200298 2,4,9,0,9,0,3,3,9,7,3,4,8,4,2,3,0,2,3,5,1,4,5,3,8,5,5,6,8,7,4
%N A200298 Decimal expansion of greatest x satisfying 4*x^2-3*cos(x)=2*sin(x).
%C A200298 See A199949 for a guide to related sequences. The Mathematica program includes a graph.
%H A200298 G. C. Greubel, <a href="/A200298/b200298.txt">Table of n, a(n) for n = 0..10000</a>
%H A200298 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A200298 least x: -0.58847086928685261649979864856036...
%e A200298 greatest x: 0.922697336548314794603906551791...
%t A200298 a = 4; b = -3; c = 2;
%t A200298 f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
%t A200298 Plot[{f[x], g[x]}, {x, -1, 1}, {AxesOrigin -> {0, 0}}]
%t A200298 r = x /. FindRoot[f[x] == g[x], {x, -.59, -.58}, WorkingPrecision -> 110]
%t A200298 RealDigits[r]   (* A200297 *)
%t A200298 r = x /. FindRoot[f[x] == g[x], {x, .92, .93}, WorkingPrecision -> 110]
%t A200298 RealDigits[r]   (* A200298 *)
%o A200298 (PARI) a=4; b=-3; c=2; solve(x=.92, .93, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jun 22 2018
%Y A200298 Cf. A199949.
%K A200298 nonn,cons
%O A200298 0,1
%A A200298 _Clark Kimberling_, Nov 15 2011