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A200286 Decimal expansion of least x satisfying 4*x^2 - cos(x) = sin(x).

%I A200286 #12 Feb 12 2025 14:33:59
%S A200286 5,8,8,8,5,1,7,4,2,6,7,5,0,4,1,1,7,9,9,9,9,6,5,9,7,1,4,6,4,4,8,4,8,0,
%T A200286 3,8,1,8,0,1,6,1,3,7,1,7,0,6,1,7,3,1,0,3,1,5,9,4,8,7,4,1,6,6,3,8,7,9,
%U A200286 2,3,6,2,6,0,5,0,4,2,8,3,7,4,8,0,4,0,8,0,9,8,6,0,4,9,9,8,2,2,7
%N A200286 Decimal expansion of least x satisfying 4*x^2 - cos(x) = sin(x).
%C A200286 See A199949 for a guide to related sequences. The Mathematica program includes a graph.
%H A200286 G. C. Greubel, <a href="/A200286/b200286.txt">Table of n, a(n) for n = 0..10000</a>
%H A200286 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A200286 least x: -0.37540364996113984869295773583715442...
%e A200286 greatest x: 0.588851742675041179999659714644848...
%t A200286 a = 4; b = -1; c = 1;
%t A200286 f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
%t A200286 Plot[{f[x], g[x]}, {x, -1, 1}, {AxesOrigin -> {0, 0}}]
%t A200286 r = x /. FindRoot[f[x] == g[x], {x, -.38, -.37}, WorkingPrecision -> 110]
%t A200286 RealDigits[r]   (* A200285 *)
%t A200286 r = x /. FindRoot[f[x] == g[x], {x, .58, .59}, WorkingPrecision -> 110]
%t A200286 RealDigits[r]   (* A200286 *)
%o A200286 (PARI) a=4; b=-1; c=1; solve(x=0, 1, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jul 07 2018
%Y A200286 Cf. A199949.
%K A200286 nonn,cons
%O A200286 0,1
%A A200286 _Clark Kimberling_, Nov 15 2011