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A200236 Decimal expansion of greatest x satisfying 3*x^2 - 2*cos(x) = 4*sin(x).

%I A200236 #14 Feb 12 2025 13:04:35
%S A200236 1,2,1,7,2,4,5,4,2,8,9,4,5,4,5,9,0,2,7,6,9,3,2,4,5,8,6,3,5,4,5,6,0,7,
%T A200236 5,9,8,0,1,4,4,3,6,1,3,7,3,3,1,6,6,6,9,9,0,4,7,4,1,7,5,2,2,5,7,9,2,2,
%U A200236 5,5,9,2,8,8,9,6,7,8,5,5,1,4,3,9,4,3,5,4,6,8,8,7,5,3,5,3,3,4,4
%N A200236 Decimal expansion of greatest x satisfying 3*x^2 - 2*cos(x) = 4*sin(x).
%C A200236 See A199949 for a guide to related sequences. The Mathematica program includes a graph.
%H A200236 G. C. Greubel, <a href="/A200236/b200236.txt">Table of n, a(n) for n = 1..10000</a>
%H A200236 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A200236 least x: -0.37112234946927280533419999688093...
%e A200236 greatest x: 1.217245428945459027693245863545...
%t A200236 a = 3; b = -2; c = 4;
%t A200236 f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
%t A200236 Plot[{f[x], g[x]}, {x, -2, 2}, {AxesOrigin -> {0, 0}}]
%t A200236 r = x /. FindRoot[f[x] == g[x], {x, -.38, -.37}, WorkingPrecision -> 110]
%t A200236 RealDigits[r]   (* A200235 *)
%t A200236 r = x /. FindRoot[f[x] == g[x], {x, 1.2, 1.3}, WorkingPrecision -> 110]
%t A200236 RealDigits[r]   (* A200236 *)
%o A200236 (PARI) a=3; b=-2; c=4; solve(x=1, 2, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jul 05 2018
%Y A200236 Cf. A199949.
%K A200236 nonn,cons
%O A200236 1,2
%A A200236 _Clark Kimberling_, Nov 14 2011