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A200234 Decimal expansion of greatest x satisfying 3*x^2 - 2*cos(x) = 3*sin(x).

%I A200234 #11 Feb 12 2025 13:04:33
%S A200234 1,0,9,2,9,6,1,3,1,2,6,1,9,6,9,4,2,6,9,6,4,3,3,8,2,9,1,2,5,5,6,6,2,2,
%T A200234 1,9,2,9,1,4,5,1,8,5,8,8,1,8,0,2,8,9,8,8,9,9,6,1,7,6,3,5,6,9,6,8,9,4,
%U A200234 4,7,6,1,6,7,6,3,4,5,1,0,2,5,1,1,5,0,5,4,3,1,2,2,5,4,0,3,8,6,4
%N A200234 Decimal expansion of greatest x satisfying 3*x^2 - 2*cos(x) = 3*sin(x).
%C A200234 See A199949 for a guide to related sequences. The Mathematica program includes a graph.
%H A200234 G. C. Greubel, <a href="/A200234/b200234.txt">Table of n, a(n) for n = 1..10000</a>
%H A200234 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A200234 least x: -0.432052760425723131996383607455372280...
%e A200234 greatest x: 1.0929613126196942696433829125566221...
%t A200234 a = 3; b = -2; c = 3;
%t A200234 f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
%t A200234 Plot[{f[x], g[x]}, {x, -2, 2}, {AxesOrigin -> {0, 0}}]
%t A200234 r = x /. FindRoot[f[x] == g[x], {x, -.44, -.43}, WorkingPrecision -> 110]
%t A200234 RealDigits[r]   (* A200233 *)
%t A200234 r = x /. FindRoot[f[x] == g[x], {x, 1.08, 1.09}, WorkingPrecision -> 110]
%t A200234 RealDigits[r]   (* A200234 *)
%o A200234 (PARI) a=3; b=-2; c=3; solve(x=1, 2, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jun 30 2018
%Y A200234 Cf. A199949.
%K A200234 nonn,cons
%O A200234 1,3
%A A200234 _Clark Kimberling_, Nov 14 2011