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A200239 Decimal expansion of least x satisfying 3*x^2-3*cos(x)=2*sin(x).

%I A200239 #15 Feb 12 2025 13:05:44
%S A200239 6,3,7,6,6,1,1,5,7,9,4,6,0,7,3,1,3,4,1,1,9,8,9,5,4,5,6,5,8,8,1,9,6,2,
%T A200239 0,1,3,7,3,3,9,9,2,2,8,0,7,2,7,3,3,8,6,9,5,5,6,1,0,6,2,3,0,9,0,1,0,1,
%U A200239 4,0,5,4,5,4,4,3,3,0,7,9,6,8,0,0,1,4,3,8,4,6,5,1,0,7,1,4,4,7,8
%N A200239 Decimal expansion of least x satisfying 3*x^2-3*cos(x)=2*sin(x).
%C A200239 See A199949 for a guide to related sequences. The Mathematica program includes a graph.
%H A200239 G. C. Greubel, <a href="/A200239/b200239.txt">Table of n, a(n) for n = 0..10000</a>
%H A200239 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A200239 least x: -0.63766115794607313411989545658819620...
%e A200239 greatest x: 1.039829693324607596071793532120387...
%t A200239 a = 3; b = -3; c = 2;
%t A200239 f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
%t A200239 Plot[{f[x], g[x]}, {x, -2, 2}, {AxesOrigin -> {0, 0}}]
%t A200239 r = x /. FindRoot[f[x] == g[x], {x, -.64, -.63}, WorkingPrecision -> 110]
%t A200239 RealDigits[r]   (* A200239 *)
%t A200239 r = x /. FindRoot[f[x] == g[x], {x, 1.0, 1.1}, WorkingPrecision -> 110]
%t A200239 RealDigits[r]   (* A200240 *)
%o A200239 (PARI) a=3; b=-3; c=2; solve(x=-.64, -.63, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jun 22 2018
%Y A200239 Cf. A199949.
%K A200239 nonn,cons
%O A200239 0,1
%A A200239 _Clark Kimberling_, Nov 15 2011