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A200099 Decimal expansion of least x satisfying x^2 - 4*cos(x) = sin(x), negated.

%I A200099 #13 Feb 12 2025 09:54:21
%S A200099 1,0,5,3,3,5,2,9,8,3,6,0,0,1,5,3,7,3,3,2,8,1,1,1,0,1,5,7,9,9,9,4,6,8,
%T A200099 4,6,4,9,7,0,2,8,5,2,7,9,2,2,5,9,2,3,5,3,4,2,2,3,2,3,5,1,9,8,5,0,7,9,
%U A200099 9,4,3,8,1,7,4,0,4,9,1,8,0,3,9,2,4,8,9,8,6,2,2,7,8,6,5,8,5,5,7
%N A200099 Decimal expansion of least x satisfying x^2 - 4*cos(x) = sin(x), negated.
%C A200099 See A199949 for a guide to related sequences. The Mathematica program includes a graph.
%H A200099 G. C. Greubel, <a href="/A200099/b200099.txt">Table of n, a(n) for n = 1..10000</a>
%H A200099 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A200099 least x:  -1.053352983600153733281110157999...
%e A200099 greatest x: 1.35457555821585784490890770164646...
%t A200099 a = 1; b = -4; c = 1;
%t A200099 f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
%t A200099 Plot[{f[x], g[x]}, {x, -3, 3}, {AxesOrigin -> {0, 0}}]
%t A200099 r = x /. FindRoot[f[x] == g[x], {x, -1.06, -1.05}, WorkingPrecision -> 110]
%t A200099 RealDigits[r]  (* A200099 *)
%t A200099 r = x /. FindRoot[f[x] == g[x], {x, 1.35, 1.36}, WorkingPrecision -> 110]
%t A200099 RealDigits[r]  (* A200100 *)
%o A200099 (PARI) a=1; b=-4; c=1; solve(x=-2, 0, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jun 24 2018
%Y A200099 Cf. A199949.
%K A200099 nonn,cons
%O A200099 1,3
%A A200099 _Clark Kimberling_, Nov 13 2011