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A200285 Decimal expansion of least x satisfying 4*x^2 - cos(x) = sin(x), negated.

%I A200285 #12 Feb 12 2025 14:33:53
%S A200285 3,7,5,4,0,3,6,4,9,9,6,1,1,3,9,8,4,8,6,9,2,9,5,7,7,3,5,8,3,7,1,5,4,4,
%T A200285 2,9,2,9,9,7,6,1,4,4,3,4,6,5,7,3,0,8,5,7,0,2,2,9,3,2,6,0,8,6,4,5,3,1,
%U A200285 4,7,9,1,5,9,0,0,2,3,7,6,2,0,0,4,8,2,8,6,4,7,6,2,8,2,4,9,1,2,5
%N A200285 Decimal expansion of least x satisfying 4*x^2 - cos(x) = sin(x), negated.
%C A200285 See A199949 for a guide to related sequences. The Mathematica program includes a graph.
%H A200285 G. C. Greubel, <a href="/A200285/b200285.txt">Table of n, a(n) for n = 0..10000</a>
%H A200285 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A200285 least x: -0.37540364996113984869295773583715442...
%e A200285 greatest x: 0.588851742675041179999659714644848...
%t A200285 a = 4; b = -1; c = 1;
%t A200285 f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
%t A200285 Plot[{f[x], g[x]}, {x, -1, 1}, {AxesOrigin -> {0, 0}}]
%t A200285 r = x /. FindRoot[f[x] == g[x], {x, -.38, -.37}, WorkingPrecision -> 110]
%t A200285 RealDigits[r]   (* A200285 *)
%t A200285 r = x /. FindRoot[f[x] == g[x], {x, .58, .59}, WorkingPrecision -> 110]
%t A200285 RealDigits[r]   (* A200286 *)
%o A200285 (PARI) a=4; b=-1; c=1; solve(x=-1, 0, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jul 07 2018
%Y A200285 Cf. A199949.
%K A200285 nonn,cons
%O A200285 0,1
%A A200285 _Clark Kimberling_, Nov 15 2011