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A200301 Decimal expansion of least x satisfying 4*x^2 - 3*cos(x) = 3*sin(x), negated.

%I A200301 #15 Feb 12 2025 14:36:07
%S A200301 5,2,3,7,7,4,1,5,6,7,5,3,2,5,5,7,2,1,7,1,7,8,4,0,4,9,6,7,3,9,4,4,5,2,
%T A200301 8,5,3,9,0,6,0,2,4,7,1,1,0,3,1,6,0,9,9,7,1,6,8,4,8,7,8,1,5,3,9,7,3,9,
%U A200301 2,9,3,2,3,9,5,9,6,2,6,5,2,2,3,5,6,8,4,2,6,0,2,5,3,5,8,7,5,3,6
%N A200301 Decimal expansion of least x satisfying 4*x^2 - 3*cos(x) = 3*sin(x), negated.
%C A200301 See A199949 for a guide to related sequences. The Mathematica program includes a graph.
%H A200301 G. C. Greubel, <a href="/A200301/b200301.txt">Table of n, a(n) for n = 0..10000</a>
%H A200301 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A200301 least x: -0.52377415675325572171784049673944...
%e A200301 greatest x: 1.01614395672355873379945590129...
%t A200301 a = 4; b = -3; c = 3;
%t A200301 f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
%t A200301 Plot[{f[x], g[x]}, {x, -1, 1}, {AxesOrigin -> {0, 0}}]
%t A200301 r = x /. FindRoot[f[x] == g[x], {x, -.54, -.51}, WorkingPrecision -> 110]
%t A200301 RealDigits[r]   (* A200297 *)
%t A200301 r = x /. FindRoot[f[x] == g[x], {x, 1, 1.03}, WorkingPrecision -> 110]
%t A200301 RealDigits[r]   (* A200298 *)
%o A200301 (PARI) a=4; b=-3; c=3; solve(x=-1, 0, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jul 08 2018
%Y A200301 Cf. A199949.
%K A200301 nonn,cons
%O A200301 0,1
%A A200301 _Clark Kimberling_, Nov 15 2011