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A200289 Decimal expansion of least x satisfying 4*x^2 - cos(x) = 3*sin(x), negated.

%I A200289 #12 Feb 12 2025 14:33:57
%S A200289 2,4,5,4,6,3,0,3,1,8,3,0,8,2,4,2,4,2,4,7,0,6,1,7,6,6,0,4,7,0,7,3,8,4,
%T A200289 5,8,1,6,4,2,5,7,7,4,2,9,7,6,4,7,9,0,9,3,7,0,2,2,5,4,1,0,9,6,0,5,9,1,
%U A200289 2,8,3,6,7,0,6,9,3,3,6,3,2,7,8,1,3,7,7,8,9,3,8,6,6,5,6,9,8,4,6
%N A200289 Decimal expansion of least x satisfying 4*x^2 - cos(x) = 3*sin(x), negated.
%C A200289 See A199949 for a guide to related sequences. The Mathematica program includes a graph.
%H A200289 G. C. Greubel, <a href="/A200289/b200289.txt">Table of n, a(n) for n = 0..10000</a>
%H A200289 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A200289 least x: -0.2454630318308242424706176604707384581...
%e A200289 greatest x: 0.85425847729971214786694703263536193...
%t A200289 a = 4; b = -1; c = 3;
%t A200289 f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
%t A200289 Plot[{f[x], g[x]}, {x, -1, 1}, {AxesOrigin -> {0, 0}}]
%t A200289 r = x /. FindRoot[f[x] == g[x], {x, -.25, -.24}, WorkingPrecision -> 110]
%t A200289 RealDigits[r]    (* A200289 *)
%t A200289 r = x /. FindRoot[f[x] == g[x], {x, .85, .86}, WorkingPrecision -> 110]
%t A200289 RealDigits[r]    (* A200290 *)
%o A200289 (PARI) a=4; b=-1; c=3; solve(x=-1, 0, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jul 07 2018
%Y A200289 Cf. A199949.
%K A200289 nonn,cons
%O A200289 0,1
%A A200289 _Clark Kimberling_, Nov 15 2011