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A200233 Decimal expansion of least x satisfying 3*x^2 - 2*cos(x) = 3*sin(x), negated.

%I A200233 #11 Feb 12 2025 13:04:25
%S A200233 4,3,2,0,5,2,7,6,0,4,2,5,7,2,3,1,3,1,9,9,6,3,8,3,6,0,7,4,5,5,3,7,2,2,
%T A200233 8,0,5,2,2,3,5,0,2,1,7,0,6,9,8,9,9,8,4,6,3,1,2,6,8,8,5,4,9,9,4,2,0,0,
%U A200233 8,9,3,8,0,5,2,1,6,6,7,1,4,8,1,7,7,7,5,4,4,3,8,3,6,7,9,0,7,0,4
%N A200233 Decimal expansion of least x satisfying 3*x^2 - 2*cos(x) = 3*sin(x), negated.
%C A200233 See A199949 for a guide to related sequences. The Mathematica program includes a graph.
%H A200233 G. C. Greubel, <a href="/A200233/b200233.txt">Table of n, a(n) for n = 0..10000</a>
%H A200233 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A200233 least x: -0.432052760425723131996383607455372280...
%e A200233 greatest x: 1.0929613126196942696433829125566221...
%t A200233 a = 3; b = -2; c = 3;
%t A200233 f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
%t A200233 Plot[{f[x], g[x]}, {x, -2, 2}, {AxesOrigin -> {0, 0}}]
%t A200233 r = x /. FindRoot[f[x] == g[x], {x, -.44, -.43}, WorkingPrecision -> 110]
%t A200233 RealDigits[r]   (* A200233 *)
%t A200233 r = x /. FindRoot[f[x] == g[x], {x, 1.08, 1.09}, WorkingPrecision -> 110]
%t A200233 RealDigits[r]   (* A200234 *)
%o A200233 (PARI) a=3; b=-2; c=3; solve(x=-1, 0, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jun 30 2018
%Y A200233 Cf. A199949.
%K A200233 nonn,cons
%O A200233 0,1
%A A200233 _Clark Kimberling_, Nov 14 2011