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A200240 Decimal expansion of greatest x satisfying 3*x^2-3*cos(x)=2*sin(x).

%I A200240 #15 Feb 12 2025 13:05:39
%S A200240 1,0,3,9,8,2,9,6,9,3,3,2,4,6,0,7,5,9,6,0,7,1,7,9,3,5,3,2,1,2,0,3,8,7,
%T A200240 7,6,2,6,4,1,3,2,0,9,3,9,9,9,6,8,7,3,4,1,4,4,0,5,9,2,6,3,0,4,7,3,9,8,
%U A200240 1,6,8,8,9,6,2,3,0,3,5,4,8,8,6,6,3,9,1,6,5,0,2,9,3,0,7,2,3,3,6
%N A200240 Decimal expansion of greatest x satisfying 3*x^2-3*cos(x)=2*sin(x).
%C A200240 See A199949 for a guide to related sequences. The Mathematica program includes a graph.
%H A200240 G. C. Greubel, <a href="/A200240/b200240.txt">Table of n, a(n) for n = 1..10000</a>
%H A200240 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A200240 least x: -0.63766115794607313411989545658819620...
%e A200240 greatest x: 1.039829693324607596071793532120387...
%t A200240 a = 3; b = -3; c = 2;
%t A200240 f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
%t A200240 Plot[{f[x], g[x]}, {x, -2, 2}, {AxesOrigin -> {0, 0}}]
%t A200240 r = x /. FindRoot[f[x] == g[x], {x, -.64, -.63}, WorkingPrecision -> 110]
%t A200240 RealDigits[r]   (* A200239 *)
%t A200240 r = x /. FindRoot[f[x] == g[x], {x, 1.0, 1.1}, WorkingPrecision -> 110]
%t A200240 RealDigits[r]   (* A200240 *)
%o A200240 (PARI) a=3; b=-3; c=2; solve(x=1.0, 1.1, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jun 22 2018
%Y A200240 Cf. A199949.
%K A200240 nonn,cons
%O A200240 1,3
%A A200240 _Clark Kimberling_, Nov 15 2011