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A200299 Decimal expansion of least x satisfying 4*x^2 - 3*cos(x) = sin(x), negated.

%I A200299 #12 Feb 12 2025 14:36:03
%S A200299 6,6,1,8,2,6,1,4,1,1,8,8,8,5,0,9,9,3,7,4,3,0,2,6,1,2,3,3,5,7,0,9,4,9,
%T A200299 8,9,9,7,5,1,0,6,5,0,4,6,2,1,0,8,6,4,2,4,6,4,5,8,2,2,2,9,2,0,0,8,7,1,
%U A200299 3,6,7,6,2,5,6,7,4,1,1,2,3,6,0,8,5,7,6,5,1,0,0,8,9,0,2,7,5,3,4
%N A200299 Decimal expansion of least x satisfying 4*x^2 - 3*cos(x) = sin(x), negated.
%C A200299 See A199949 for a guide to related sequences. The Mathematica program includes a graph.
%H A200299 G. C. Greubel, <a href="/A200299/b200299.txt">Table of n, a(n) for n = 0..10000</a>
%H A200299 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A200299 least x: -0.661826141188850993743026123357094...
%e A200299 greatest x: 0.8308503276605474027666209935665...
%t A200299 a = 4; b = -3; c = 1;
%t A200299 f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
%t A200299 Plot[{f[x], g[x]}, {x, -1, 1}, {AxesOrigin -> {0, 0}}]
%t A200299 r = x /. FindRoot[f[x] == g[x], {x, -.67, -.66}, WorkingPrecision -> 110]
%t A200299 RealDigits[r]   (* A200299 *)
%t A200299 r = x /. FindRoot[f[x] == g[x], {x, .83, .84}, WorkingPrecision -> 110]
%t A200299 RealDigits[r]   (* A200300 *)
%o A200299 (PARI) a=4; b=-3; c=1; solve(x=-1, 0, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jul 08 2018
%Y A200299 Cf. A199949.
%K A200299 nonn,cons
%O A200299 0,1
%A A200299 _Clark Kimberling_, Nov 15 2011