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A200292 Decimal expansion of greatest x satisfying 4*x^2 - cos(x) = 4*sin(x).

%I A200292 #11 Feb 12 2025 14:35:05
%S A200292 9,8,5,7,7,6,3,8,1,7,0,3,9,0,0,4,5,5,0,3,0,7,9,4,0,5,3,8,7,9,8,1,9,7,
%T A200292 0,2,6,4,6,4,5,4,7,6,8,0,5,5,7,6,8,2,0,7,6,9,5,1,3,0,6,1,3,2,4,7,8,8,
%U A200292 7,1,1,4,4,3,5,5,7,6,3,0,7,3,6,6,1,0,7,1,6,8,3,1,1,7,4,8,2,1,5
%N A200292 Decimal expansion of greatest x satisfying 4*x^2 - cos(x) = 4*sin(x).
%C A200292 See A199949 for a guide to related sequences. The Mathematica program includes a graph.
%H A200292 G. C. Greubel, <a href="/A200292/b200292.txt">Table of n, a(n) for n = 0..10000</a>
%H A200292 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A200292 least x: -0.2044255015377807131364929398797955...
%e A200292 greatest x: 0.98577638170390045503079405387981...
%t A200292 a = 4; b = -1; c = 4;
%t A200292 f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
%t A200292 Plot[{f[x], g[x]}, {x, -1, 1}, {AxesOrigin -> {0, 0}}]
%t A200292 r = x /. FindRoot[f[x] == g[x], {x, -.21, -.20}, WorkingPrecision -> 110]
%t A200292 RealDigits[r]    (* A200291 *)
%t A200292 r = x /. FindRoot[f[x] == g[x], {x, .98, .99}, WorkingPrecision -> 110]
%t A200292 RealDigits[r]   (* A200292 *)
%o A200292 (PARI) a=4; b=-1; c=4; solve(x=0, 1, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jul 08 2018
%Y A200292 Cf. A199949.
%K A200292 nonn,cons
%O A200292 0,1
%A A200292 _Clark Kimberling_, Nov 15 2011