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A200294 Decimal expansion of greatest x satisfying 4*x^2 - 2*cos(x) = sin(x).

%I A200294 #12 Feb 12 2025 14:35:08
%S A200294 7,3,3,9,7,2,6,2,7,9,4,0,2,8,9,6,1,4,3,3,4,5,0,5,0,5,6,0,0,3,9,2,9,9,
%T A200294 2,2,0,8,5,4,5,1,3,5,6,9,6,3,5,3,9,8,1,5,0,7,6,2,5,5,4,7,2,6,5,7,2,8,
%U A200294 2,7,5,2,5,7,8,5,8,9,3,8,3,1,7,1,7,4,0,3,8,2,6,2,1,8,4,2,6,9,5
%N A200294 Decimal expansion of greatest x satisfying 4*x^2 - 2*cos(x) = sin(x).
%C A200294 See A199949 for a guide to related sequences. The Mathematica program includes a graph.
%H A200294 G. C. Greubel, <a href="/A200294/b200294.txt">Table of n, a(n) for n = 0..10000</a>
%H A200294 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A200294 least x: -0.5455973884814757395042148847857...
%e A200294 greatest x: 0.73397262794028961433450505600...
%t A200294 a = 4; b = -2; c = 1;
%t A200294 f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
%t A200294 Plot[{f[x], g[x]}, {x, -1, 1}, {AxesOrigin -> {0, 0}}]
%t A200294 r = x /. FindRoot[f[x] == g[x], {x, -.55, -.54}, WorkingPrecision -> 110]
%t A200294 RealDigits[r]   (* A200293 *)
%t A200294 r = x /. FindRoot[f[x] == g[x], {x, .73, .74}, WorkingPrecision -> 110]
%t A200294 RealDigits[r]   (* A200294 *)
%o A200294 (PARI) a=4; b=-2; c=1; solve(x=0, 1, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jul 08 2018
%Y A200294 Cf. A199949.
%K A200294 nonn,cons
%O A200294 0,1
%A A200294 _Clark Kimberling_, Nov 15 2011