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A200014 Decimal expansion of least x satisfying x^2 - cos(x) = 3*sin(x), negated.

%I A200014 #14 Feb 12 2025 04:52:40
%S A200014 2,9,4,3,4,8,7,7,2,3,3,5,6,8,6,3,9,8,3,6,9,6,5,7,8,9,0,2,0,3,6,1,9,5,
%T A200014 0,3,0,8,6,7,2,1,9,9,0,0,5,9,4,0,0,3,2,8,8,8,6,8,4,1,8,0,1,6,5,1,9,9,
%U A200014 9,8,1,5,0,7,0,7,8,4,3,8,3,5,7,8,4,4,7,6,2,2,5,3,2,2,6,0,3,9,8
%N A200014 Decimal expansion of least x satisfying x^2 - cos(x) = 3*sin(x), negated.
%C A200014 See A199949 for a guide to related sequences. The Mathematica program includes a graph.
%H A200014 G. C. Greubel, <a href="/A200014/b200014.txt">Table of n, a(n) for n = 0..10000</a>
%H A200014 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A200014 least x:  -0.2943487723356863983696578902036195...
%e A200014 greatest x: 1.690779738969815334957504857558809...
%t A200014 a = 1; b = -1; c = 3;
%t A200014 f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
%t A200014 Plot[{f[x], g[x]}, {x, -1, 2}, {AxesOrigin -> {0, 0}}]
%t A200014 r = x /. FindRoot[f[x] == g[x], {x, -.3, -.29}, WorkingPrecision -> 110]
%t A200014 RealDigits[r]  (* A200014 *)
%t A200014 r = x /. FindRoot[f[x] == g[x], {x, 1.6, 1.7}, WorkingPrecision -> 110]
%t A200014 RealDigits[r]   (* A200015 *)
%o A200014 (PARI) a=1; b=-1; c=3; solve(x=-1, 0, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jun 23 2018
%Y A200014 Cf. A199949.
%K A200014 nonn,cons
%O A200014 0,1
%A A200014 _Clark Kimberling_, Nov 12 2011