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A200235 Decimal expansion of least x satisfying 3*x^2 - 2*cos(x) = 4*sin(x), negated.

%I A200235 #14 Feb 12 2025 13:04:26
%S A200235 3,7,1,1,2,2,3,4,9,4,6,9,2,7,2,8,0,5,3,3,4,1,9,9,9,9,6,8,8,0,9,3,8,5,
%T A200235 6,5,6,5,1,2,3,2,4,3,8,8,6,7,4,2,5,0,8,9,6,7,6,3,4,5,2,4,2,0,1,5,5,2,
%U A200235 9,8,3,5,9,4,0,9,7,0,6,9,2,5,8,1,2,3,2,9,9,9,3,5,7,3,5,1,3,4,1
%N A200235 Decimal expansion of least x satisfying 3*x^2 - 2*cos(x) = 4*sin(x), negated.
%C A200235 See A199949 for a guide to related sequences. The Mathematica program includes a graph.
%H A200235 G. C. Greubel, <a href="/A200235/b200235.txt">Table of n, a(n) for n = 0..10000</a>
%H A200235 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A200235 least x: -0.37112234946927280533419999688093...
%e A200235 greatest x: 1.217245428945459027693245863545...
%t A200235 a = 3; b = -2; c = 4;
%t A200235 f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
%t A200235 Plot[{f[x], g[x]}, {x, -2, 2}, {AxesOrigin -> {0, 0}}]
%t A200235 r = x /. FindRoot[f[x] == g[x], {x, -.38, -.37}, WorkingPrecision -> 110]
%t A200235 RealDigits[r]   (* A200235 *)
%t A200235 r = x /. FindRoot[f[x] == g[x], {x, 1.2, 1.3}, WorkingPrecision -> 110]
%t A200235 RealDigits[r]   (* A200236 *)
%o A200235 (PARI) a=3; b=-2; c=4; solve(x=-1, 0, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jul 05 2018
%Y A200235 Cf. A199949.
%K A200235 nonn,cons
%O A200235 0,1
%A A200235 _Clark Kimberling_, Nov 14 2011