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A199966 Decimal expansion of greatest x satisfying x^2 + 4*cos(x) = 4*sin(x).

%I A199966 #15 Feb 11 2025 22:47:54
%S A199966 2,3,7,8,1,2,8,1,6,8,6,7,3,7,6,7,9,8,5,9,6,8,2,0,1,6,6,1,4,7,2,8,8,6,
%T A199966 2,1,5,3,6,6,2,9,9,9,1,5,8,9,3,5,4,1,0,0,2,2,0,8,2,0,2,7,0,8,1,3,7,4,
%U A199966 7,2,2,3,6,2,6,6,4,9,9,0,1,2,4,6,4,8,9,3,9,4,0,0,3,4,4,9,9,2,7
%N A199966 Decimal expansion of greatest x satisfying x^2 + 4*cos(x) = 4*sin(x).
%C A199966 See A199949 for a guide to related sequences. The Mathematica program includes a graph.
%H A199966 G. C. Greubel, <a href="/A199966/b199966.txt">Table of n, a(n) for n = 1..10000</a>
%H A199966 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A199966 least x:  0.943379571591794622084167020515639838...
%e A199966 greatest x: 2.3781281686737679859682016614728862...
%t A199966 a = 1; b = 4; c = 4;
%t A199966 f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
%t A199966 Plot[{f[x], g[x]}, {x, -1, 3}, {AxesOrigin -> {0, 0}}]
%t A199966 r = x /. FindRoot[f[x] == g[x], {x, .94, .95}, WorkingPrecision -> 110]
%t A199966 RealDigits[r]  (* A199965 *)
%t A199966 r = x /. FindRoot[f[x] == g[x], {x, 2.37, 2.38}, WorkingPrecision -> 110]
%t A199966 RealDigits[r]  (* A199966 *)
%o A199966 (PARI) a=1; b=4; c=4; solve(x=2, 3, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jun 23 2018
%Y A199966 Cf. A199949.
%K A199966 nonn,cons
%O A199966 1,1
%A A199966 _Clark Kimberling_, Nov 12 2011