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A200097 Decimal expansion of least x satisfying x^2 - 3*cos(x) = 4*sin(x), negated.

%I A200097 #13 Feb 12 2025 09:53:23
%S A200097 5,7,6,8,9,1,1,7,6,9,6,2,1,8,6,4,3,5,7,5,2,4,3,6,5,9,7,7,1,8,2,6,1,6,
%T A200097 8,8,1,3,0,0,1,4,9,2,6,4,9,3,8,9,4,3,7,3,7,0,9,4,4,4,3,6,3,0,1,9,9,8,
%U A200097 0,5,6,2,7,8,9,7,6,0,4,1,7,0,4,0,7,2,5,0,1,3,7,5,2,3,3,7,1,0,6
%N A200097 Decimal expansion of least x satisfying x^2 - 3*cos(x) = 4*sin(x), negated.
%C A200097 See A199949 for a guide to related sequences. The Mathematica program includes a graph.
%H A200097 G. C. Greubel, <a href="/A200097/b200097.txt">Table of n, a(n) for n = 0..10000</a>
%H A200097 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A200097 least x:  -0.576891176962186435752436597718261688130...
%e A200097 greatest x: 1.79646741863500842707885236614949093773...
%t A200097 a = 1; b = -3; c = 4;
%t A200097 f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
%t A200097 Plot[{f[x], g[x]}, {x, -3, 3}, {AxesOrigin -> {0, 0}}]
%t A200097 r = x /. FindRoot[f[x] == g[x], {x, -.58, -.57}, WorkingPrecision -> 110]
%t A200097 RealDigits[r]  (* A200097 *)
%t A200097 r = x /. FindRoot[f[x] == g[x], {x, 1.79, 1.80}, WorkingPrecision -> 110]
%t A200097 RealDigits[r]  (* A200098 *)
%o A200097 (PARI) a=1; b=-3; c=4; solve(x=-1, 0, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jun 24 2018
%Y A200097 Cf. A199949.
%K A200097 nonn,cons
%O A200097 0,1
%A A200097 _Clark Kimberling_, Nov 13 2011