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A200293 Decimal expansion of least x satisfying 4*x^2 - 2*cos(x) = sin(x), negated.

%I A200293 #12 Feb 12 2025 14:35:00
%S A200293 5,4,5,5,9,7,3,8,8,4,8,1,4,7,5,7,3,9,5,0,4,2,1,4,8,8,4,7,8,5,7,7,0,8,
%T A200293 2,9,5,6,7,1,6,1,0,9,4,3,0,5,0,7,0,8,5,7,7,6,2,5,1,5,3,7,5,2,4,9,3,9,
%U A200293 3,1,6,9,6,6,6,8,7,1,7,6,5,7,1,8,2,1,1,6,7,3,3,3,3,5,7,9,4,4,5
%N A200293 Decimal expansion of least x satisfying 4*x^2 - 2*cos(x) = sin(x), negated.
%C A200293 See A199949 for a guide to related sequences. The Mathematica program includes a graph.
%H A200293 G. C. Greubel, <a href="/A200293/b200293.txt">Table of n, a(n) for n = 0..10000</a>
%H A200293 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A200293 least x: -0.5455973884814757395042148847857...
%e A200293 greatest x: 0.73397262794028961433450505600...
%t A200293 a = 4; b = -2; c = 1;
%t A200293 f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
%t A200293 Plot[{f[x], g[x]}, {x, -1, 1}, {AxesOrigin -> {0, 0}}]
%t A200293 r = x /. FindRoot[f[x] == g[x], {x, -.55, -.54}, WorkingPrecision -> 110]
%t A200293 RealDigits[r]   (* A200293 *)
%t A200293 r = x /. FindRoot[f[x] == g[x], {x, .73, .74}, WorkingPrecision -> 110]
%t A200293 RealDigits[r]   (* A200294 *)
%o A200293 (PARI) a=4; b=-2; c=1; solve(x=-1, 0, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jul 08 2018
%Y A200293 Cf. A199949.
%K A200293 nonn,cons
%O A200293 0,1
%A A200293 _Clark Kimberling_, Nov 15 2011