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A200284 Decimal expansion of greatest x satisfying 3*x^2 - 4*cos(x) = 4*sin(x), negated.

%I A200284 #15 Feb 12 2025 14:33:04
%S A200284 1,2,8,6,1,2,8,0,2,6,7,4,5,9,0,9,9,6,5,2,7,9,1,5,1,1,2,6,1,4,6,3,7,9,
%T A200284 4,2,3,5,1,2,6,4,2,7,5,6,5,2,8,4,4,1,9,4,6,0,0,6,6,9,7,2,2,3,6,1,3,0,
%U A200284 5,8,2,2,0,3,8,5,4,0,6,3,0,8,7,8,1,6,4,5,6,4,8,4,3,6,3,8,2,8,2
%N A200284 Decimal expansion of greatest x satisfying 3*x^2 - 4*cos(x) = 4*sin(x), negated.
%C A200284 See A199949 for a guide to related sequences. The Mathematica program includes a graph.
%H A200284 G. C. Greubel, <a href="/A200284/b200284.txt">Table of n, a(n) for n = 1..10000</a>
%H A200284 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A200284 least x: -0.5959294541202234263223480673526214...
%e A200284 greatest x: 1.28612802674590996527915112614637...
%t A200284 a = 3; b = -4; c = 4;
%t A200284 f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
%t A200284 Plot[{f[x], g[x]}, {x, -2, 2}, {AxesOrigin -> {0, 0}}]
%t A200284 r = x /. FindRoot[f[x] == g[x], {x, -.6, -.59}, WorkingPrecision -> 110]
%t A200284 RealDigits[r]    (* A200283 *)
%t A200284 r = x /. FindRoot[f[x] == g[x], {x, 1.2, 1.3}, WorkingPrecision -> 110]
%t A200284 RealDigits[r]   (* A200284 *)
%o A200284 (PARI) a=3; b=-4; c=4; solve(x=-1, 0, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jul 07 2018
%Y A200284 Cf. A199949.
%K A200284 nonn,cons
%O A200284 1,2
%A A200284 _Clark Kimberling_, Nov 15 2011