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A200282 Decimal expansion of greatest x satisfying 3*x^2 - 4*cos(x) = 3*sin(x).

%I A200282 #12 Feb 12 2025 14:33:02
%S A200282 1,1,9,2,4,0,4,5,5,0,0,7,6,8,1,5,6,5,9,2,9,0,0,9,5,4,9,6,6,1,3,6,9,0,
%T A200282 6,9,9,6,9,8,5,2,7,5,5,6,4,2,1,0,0,3,5,5,4,4,8,2,3,5,9,1,8,3,1,4,6,8,
%U A200282 9,9,9,4,8,6,2,2,0,2,9,2,8,7,6,5,4,6,6,0,4,1,8,0,2,4,6,8,3,0,1
%N A200282 Decimal expansion of greatest x satisfying 3*x^2 - 4*cos(x) = 3*sin(x).
%C A200282 See A199949 for a guide to related sequences. The Mathematica program includes a graph.
%H A200282 G. C. Greubel, <a href="/A200282/b200282.txt">Table of n, a(n) for n = 1..10000</a>
%H A200282 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A200282 least x: -0.6615723781879899920628993073289...
%e A200282 greatest x: 1.19240455007681565929009549661...
%t A200282 a = 3; b = -4; c = 3;
%t A200282 f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
%t A200282 Plot[{f[x], g[x]}, {x, -2, 2}, {AxesOrigin -> {0, 0}}]
%t A200282 r = x /. FindRoot[f[x] == g[x], {x, -.67, -.66}, WorkingPrecision -> 110]
%t A200282 RealDigits[r]    (* A200281 *)
%t A200282 r = x /. FindRoot[f[x] == g[x], {x, 1.1, 1.2}, WorkingPrecision -> 110]
%t A200282 RealDigits[r]   (* A200282 *)
%o A200282 (PARI) a=3; b=-4; c=3; solve(x=1, 2, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jul 07 2018
%Y A200282 Cf. A199949.
%K A200282 nonn,cons
%O A200282 1,3
%A A200282 _Clark Kimberling_, Nov 15 2011