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A200126 Decimal expansion of least x satisfying 2*x^2 - 3*cos(x) = 4*sin(x), negated.

%I A200126 #12 Feb 12 2025 13:01:11
%S A200126 5,3,0,6,3,3,0,4,7,4,9,6,8,4,8,8,8,0,1,6,6,8,0,4,1,7,5,6,7,1,0,6,4,1,
%T A200126 0,0,2,8,1,6,1,9,5,6,3,6,8,5,3,5,6,4,4,6,1,4,8,4,3,4,2,1,2,0,9,6,5,7,
%U A200126 3,0,5,4,4,1,6,7,8,8,8,3,6,3,9,5,4,1,6,4,1,4,1,5,8,8,6,7,2,2,6
%N A200126 Decimal expansion of least x satisfying 2*x^2 - 3*cos(x) = 4*sin(x), negated.
%C A200126 See A199949 for a guide to related sequences. The Mathematica program includes a graph.
%H A200126 G. C. Greubel, <a href="/A200126/b200126.txt">Table of n, a(n) for n = 0..10000</a>
%H A200126 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A200126 least x: -0.530633047496848880166804175671064100...
%e A200126 greatest x: 1.4652353861426318569459268305726949...
%t A200126 a = 2; b = -3; c = 4;
%t A200126 f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
%t A200126 Plot[{f[x], g[x]}, {x, -3, 3}, {AxesOrigin -> {0, 0}}]
%t A200126 r = x /. FindRoot[f[x] == g[x], {x, -.54, -.53}, WorkingPrecision -> 110]
%t A200126 RealDigits[r]  (* A200126 *)
%t A200126 r = x /. FindRoot[f[x] == g[x], {x, 1.46, 1.47}, WorkingPrecision -> 110]
%t A200126 RealDigits[r]  (* A200127 *)
%o A200126 (PARI) a=2; b=-3; c=4; solve(x=-1, 0, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jul 01 2018
%Y A200126 Cf. A199949.
%K A200126 nonn,cons
%O A200126 0,1
%A A200126 _Clark Kimberling_, Nov 14 2011