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A199965 Decimal expansion of least x satisfying x^2 + 4*cos(x) = 4*sin(x).

%I A199965 #15 Feb 11 2025 22:47:51
%S A199965 9,4,3,3,7,9,5,7,1,5,9,1,7,9,4,6,2,2,0,8,4,1,6,7,0,2,0,5,1,5,6,3,9,8,
%T A199965 3,8,6,1,9,2,7,5,7,1,7,2,6,5,9,1,0,4,8,4,0,1,9,0,9,2,2,8,9,2,7,0,3,8,
%U A199965 2,6,3,8,9,2,0,0,2,3,9,8,2,6,4,6,2,1,3,8,9,7,9,5,0,7,5,4,5,6,0
%N A199965 Decimal expansion of least x satisfying x^2 + 4*cos(x) = 4*sin(x).
%C A199965 See A199949 for a guide to related sequences. The Mathematica program includes a graph.
%H A199965 G. C. Greubel, <a href="/A199965/b199965.txt">Table of n, a(n) for n = 0..10000</a>
%H A199965 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A199965 least x:  0.943379571591794622084167020515639838...
%e A199965 greatest x: 2.3781281686737679859682016614728862...
%t A199965 a = 1; b = 4; c = 4;
%t A199965 f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
%t A199965 Plot[{f[x], g[x]}, {x, -1, 3}, {AxesOrigin -> {0, 0}}]
%t A199965 r = x /. FindRoot[f[x] == g[x], {x, .94, .95}, WorkingPrecision -> 110]
%t A199965 RealDigits[r]  (* A199965 *)
%t A199965 r = x /. FindRoot[f[x] == g[x], {x, 2.37, 2.38}, WorkingPrecision -> 110]
%t A199965 RealDigits[r]  (* A199966 *)
%o A199965 (PARI) a=1; b=4; c=4; solve(x=0, 1, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jun 23 2018
%Y A199965 Cf. A199949.
%K A199965 nonn,cons
%O A199965 0,1
%A A199965 _Clark Kimberling_, Nov 12 2011