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A200105 Decimal expansion of least x satisfying x^2 - 4*cos(x) = 4*sin(x), negated.

%I A200105 #11 Feb 12 2025 09:55:25
%S A200105 6,9,8,9,3,3,6,0,4,7,3,2,9,0,3,3,0,9,3,3,7,9,8,9,5,4,4,7,3,3,5,6,7,9,
%T A200105 5,6,2,3,3,5,7,2,4,8,5,1,5,7,6,1,0,5,7,8,0,2,5,6,9,3,4,7,2,6,5,4,9,7,
%U A200105 8,8,3,8,4,7,5,3,2,4,6,6,6,4,5,4,3,4,0,8,3,2,6,4,0,4,9,2,3,4,3
%N A200105 Decimal expansion of least x satisfying x^2 - 4*cos(x) = 4*sin(x), negated.
%C A200105 See A199949 for a guide to related sequences. The Mathematica program includes a graph.
%H A200105 G. C. Greubel, <a href="/A200105/b200105.txt">Table of n, a(n) for n = 0..10000</a>
%H A200105 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A200105 least x: -0.698933604732903309337989544733567956233...
%e A200105 greatest x: 1.7695688743727017491150784620016277547...
%t A200105 a = 1; b = -4; c = 4;
%t A200105 f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
%t A200105 Plot[{f[x], g[x]}, {x, -3, 3}, {AxesOrigin -> {0, 0}}]
%t A200105 r = x /. FindRoot[f[x] == g[x], {x, -.7, -.6}, WorkingPrecision -> 110]
%t A200105 RealDigits[r]  (* A200105 *)
%t A200105 r = x /. FindRoot[f[x] == g[x], {x, 1.76, 1.77}, WorkingPrecision -> 110]
%t A200105 RealDigits[r]  (* A200106 *)
%o A200105 (PARI) a=1; b=-4; c=4; solve(x=-1, 0, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jun 25 2018
%Y A200105 Cf. A199949.
%K A200105 nonn,cons
%O A200105 0,1
%A A200105 _Clark Kimberling_, Nov 13 2011