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A200295 Decimal expansion of least x satisfying 4*x^2 - 2*cos(x) = 3*sin(x), negated.

%I A200295 #12 Feb 12 2025 14:35:03
%S A200295 4,0,5,0,0,7,1,4,9,6,7,3,3,0,6,8,1,3,5,3,0,1,0,1,2,5,6,3,6,7,3,0,1,2,
%T A200295 9,4,7,4,7,4,6,9,7,5,9,6,2,6,2,8,2,3,1,1,5,4,6,1,0,3,4,9,1,3,8,3,3,9,
%U A200295 0,8,0,9,3,5,8,3,8,0,4,1,8,0,5,9,0,0,8,1,2,7,9,6,0,9,3,2,7,2,3
%N A200295 Decimal expansion of least x satisfying 4*x^2 - 2*cos(x) = 3*sin(x), negated.
%C A200295 See A199949 for a guide to related sequences. The Mathematica program includes a graph.
%H A200295 G. C. Greubel, <a href="/A200295/b200295.txt">Table of n, a(n) for n = 0..10000</a>
%H A200295 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A200295 least x: -0.40500714967330681353010125636730...
%e A200295 greatest x: 0.949145719423009844818919670857...
%t A200295 a = 4; b = -2; c = 3;
%t A200295 f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
%t A200295 Plot[{f[x], g[x]}, {x, -1, 1}, {AxesOrigin -> {0, 0}}]
%t A200295 r = x /. FindRoot[f[x] == g[x], {x, -.41, -.40}, WorkingPrecision -> 110]
%t A200295 RealDigits[r]   (* A200295 *)
%t A200295 r = x /. FindRoot[f[x] == g[x], {x, .94, .95}, WorkingPrecision -> 110]
%t A200295 RealDigits[r]   (* A200296 *)
%o A200295 (PARI) a=4; b=-2; c=3; solve(x=-1, 0, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jul 08 2018
%Y A200295 Cf. A199949.
%K A200295 nonn,cons
%O A200295 0,1
%A A200295 _Clark Kimberling_, Nov 15 2011