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A200229 Decimal expansion of least x satisfying 3*x^2 - 2*cos(x) = sin(x), negated.

%I A200229 #11 Feb 12 2025 13:04:17
%S A200229 6,0,1,0,8,4,6,0,8,5,4,4,7,4,4,5,7,8,0,8,4,0,9,1,5,7,5,7,9,3,7,9,2,4,
%T A200229 3,7,0,9,6,4,9,2,5,9,9,3,5,3,1,9,7,6,9,7,2,6,3,5,3,5,4,8,0,6,8,5,1,4,
%U A200229 2,3,0,5,2,9,4,8,1,1,0,4,5,6,6,1,1,3,2,2,1,0,5,2,6,2,2,3,1,5,1
%N A200229 Decimal expansion of least x satisfying 3*x^2 - 2*cos(x) = sin(x), negated.
%C A200229 See A199949 for a guide to related sequences. The Mathematica program includes a graph.
%H A200229 G. C. Greubel, <a href="/A200229/b200229.txt">Table of n, a(n) for n = 0..10000</a>
%H A200229 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A200229 least x: -0.6010846085447445780840915757937924370...
%e A200229 greatest x: 0.83362047030745407827417017871253212...
%t A200229 a = 3; b = -2; c = 1;
%t A200229 f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
%t A200229 Plot[{f[x], g[x]}, {x, -2, 2}, {AxesOrigin -> {0, 0}}]
%t A200229 r = x /. FindRoot[f[x] == g[x], {x, -.61, -.60}, WorkingPrecision -> 110]
%t A200229 RealDigits[r]   (* A200229 *)
%t A200229 r = x /. FindRoot[f[x] == g[x], {x, .83, .84}, WorkingPrecision -> 110]
%t A200229 RealDigits[r]   (* A200230 *)
%o A200229 (PARI) a=3; b=-2; c=1; solve(x=-1, 0, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jun 30 2018
%Y A200229 Cf. A199949.
%K A200229 nonn,cons
%O A200229 0,1
%A A200229 _Clark Kimberling_, Nov 14 2011