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A200291 Decimal expansion of least x satisfying 4*x^2 - cos(x) = 4*sin(x), negated.

%I A200291 #11 Feb 12 2025 14:34:59
%S A200291 2,0,4,4,2,5,5,0,1,5,3,7,7,8,0,7,1,3,1,3,6,4,9,2,9,3,9,8,7,9,7,9,5,5,
%T A200291 2,5,2,4,5,8,6,8,5,1,0,3,1,2,4,5,4,0,5,4,4,6,4,0,5,5,3,1,6,6,9,9,0,1,
%U A200291 8,8,2,2,8,9,3,8,5,8,2,1,8,9,8,6,8,7,3,2,9,6,3,6,5,1,7,0,3,1,8
%N A200291 Decimal expansion of least x satisfying 4*x^2 - cos(x) = 4*sin(x), negated.
%C A200291 See A199949 for a guide to related sequences. The Mathematica program includes a graph.
%H A200291 G. C. Greubel, <a href="/A200291/b200291.txt">Table of n, a(n) for n = 0..10000</a>
%H A200291 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A200291 least x: -0.2044255015377807131364929398797955...
%e A200291 greatest x: 0.98577638170390045503079405387981...
%t A200291 a = 4; b = -1; c = 4;
%t A200291 f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
%t A200291 Plot[{f[x], g[x]}, {x, -1, 1}, {AxesOrigin -> {0, 0}}]
%t A200291 r = x /. FindRoot[f[x] == g[x], {x, -.21, -.20}, WorkingPrecision -> 110]
%t A200291 RealDigits[r]    (* A200291 *)
%t A200291 r = x /. FindRoot[f[x] == g[x], {x, .98, .99}, WorkingPrecision -> 110]
%t A200291 RealDigits[r]   (* A200292 *)
%o A200291 (PARI) a=4; b=-1; c=4; solve(x=-1, 0, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jul 08 2018
%Y A200291 Cf. A199949.
%K A200291 nonn,cons
%O A200291 0,1
%A A200291 _Clark Kimberling_, Nov 15 2011