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A200281 Decimal expansion of least x satisfying 3*x^2 - 4*cos(x) = 3*sin(x), negated.

%I A200281 #12 Feb 12 2025 14:32:52
%S A200281 6,6,1,5,7,2,3,7,8,1,8,7,9,8,9,9,9,2,0,6,2,8,9,9,3,0,7,3,2,8,9,8,9,3,
%T A200281 6,5,5,7,5,7,4,9,6,3,1,7,5,0,6,4,6,6,2,7,2,2,8,7,0,8,1,1,3,0,6,7,7,3,
%U A200281 1,5,1,9,9,2,2,4,8,9,9,0,3,6,0,5,1,0,4,4,8,7,6,9,7,6,4,8,7,1,4
%N A200281 Decimal expansion of least x satisfying 3*x^2 - 4*cos(x) = 3*sin(x), negated.
%C A200281 See A199949 for a guide to related sequences. The Mathematica program includes a graph.
%H A200281 G. C. Greubel, <a href="/A200281/b200281.txt">Table of n, a(n) for n = 0..10000</a>
%H A200281 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A200281 least x: -0.6615723781879899920628993073289...
%e A200281 greatest x: 1.19240455007681565929009549661...
%t A200281 a = 3; b = -4; c = 3;
%t A200281 f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
%t A200281 Plot[{f[x], g[x]}, {x, -2, 2}, {AxesOrigin -> {0, 0}}]
%t A200281 r = x /. FindRoot[f[x] == g[x], {x, -.67, -.66}, WorkingPrecision -> 110]
%t A200281 RealDigits[r]    (* A200281 *)
%t A200281 r = x /. FindRoot[f[x] == g[x], {x, 1.1, 1.2}, WorkingPrecision -> 110]
%t A200281 RealDigits[r]   (* A200282 *)
%o A200281 (PARI) a=3; b=-4; c=3; solve(x=-1, 0, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jul 07 2018
%Y A200281 Cf. A199949.
%K A200281 nonn,cons
%O A200281 0,1
%A A200281 _Clark Kimberling_, Nov 15 2011