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A200305 Decimal expansion of least x satisfying 4*x^2 - 4*cos(x) = sin(x), negated.

%I A200305 #14 Feb 12 2025 14:37:10
%S A200305 7,4,9,4,8,3,5,5,6,2,5,9,1,5,5,2,2,3,5,6,8,3,6,3,4,8,7,7,3,5,7,9,3,9,
%T A200305 4,2,5,6,2,1,5,9,3,5,7,9,4,4,7,1,3,3,2,7,9,6,9,0,6,5,2,0,9,0,1,8,1,8,
%U A200305 6,4,0,1,2,0,3,7,3,4,3,2,7,4,0,6,6,0,2,3,8,2,0,8,4,7,3,7,2,9,6
%N A200305 Decimal expansion of least x satisfying 4*x^2 - 4*cos(x) = sin(x), negated.
%C A200305 See A199949 for a guide to related sequences. The Mathematica program includes a graph.
%H A200305 G. C. Greubel, <a href="/A200305/b200305.txt">Table of n, a(n) for n = 0..10000</a>
%H A200305 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A200305 least x: -0.749483556259155223568363487735793...
%e A200305 greatest x: 0.90305961390486425091022746455261...
%t A200305 a = 4; b = -4; c = 1;
%t A200305 f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
%t A200305 Plot[{f[x], g[x]}, {x, -2, 2}, {AxesOrigin -> {0, 0}}]
%t A200305 r = x /. FindRoot[f[x] == g[x], {x, -.75, -.74}, WorkingPrecision -> 110]
%t A200305 RealDigits[r]   (* A200305 *)
%t A200305 r = x /. FindRoot[f[x] == g[x], {x, .90, .91}, WorkingPrecision -> 110]
%t A200305 RealDigits[r]    (* A200306 *)
%o A200305 (PARI) a=4; b=-4; c=1; solve(x=-1, 0, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jul 08 2018
%Y A200305 Cf. A199949.
%K A200305 nonn,cons
%O A200305 0,1
%A A200305 _Clark Kimberling_, Nov 16 2011