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A200238 Decimal expansion of greatest x satisfying 3*x^2 - 3*cos(x) = sin(x).

%I A200238 #12 Feb 12 2025 13:08:52
%S A200238 9,3,0,0,5,7,1,1,0,0,9,2,4,8,9,2,4,6,7,8,8,2,4,6,8,1,4,4,0,5,6,4,2,9,
%T A200238 8,7,6,1,2,8,2,5,6,1,0,1,9,3,3,3,0,7,7,4,3,6,2,1,4,0,0,8,2,0,5,2,4,8,
%U A200238 3,3,0,7,8,7,5,2,4,1,7,9,3,2,7,7,1,6,9,0,3,3,2,7,7,5,3,4,1,1,2
%N A200238 Decimal expansion of greatest x satisfying 3*x^2 - 3*cos(x) = sin(x).
%C A200238 See A199949 for a guide to related sequences. The Mathematica program includes a graph.
%H A200238 G. C. Greubel, <a href="/A200238/b200238.txt">Table of n, a(n) for n = 0..10000</a>
%H A200238 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A200238 least x: -0.725773931375098148951813264652313...
%e A200238 greatest x: 0.9300571100924892467882468144056...
%t A200238 a = 3; b = -3; c = 1;
%t A200238 f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
%t A200238 Plot[{f[x], g[x]}, {x, -2, 2}, {AxesOrigin -> {0, 0}}]
%t A200238 r = x /. FindRoot[f[x] == g[x], {x, -.73, -.72}, WorkingPrecision -> 110]
%t A200238 RealDigits[r]   (* A200237 *)
%t A200238 r = x /. FindRoot[f[x] == g[x], {x, .93, .94}, WorkingPrecision -> 110]
%t A200238 RealDigits[r]   (* A200238 *)
%o A200238 (PARI) a=3; b=-3; c=1; solve(x=0, 1, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jul 05 2018
%Y A200238 Cf. A199949.
%K A200238 nonn,cons
%O A200238 0,1
%A A200238 _Clark Kimberling_, Nov 15 2011