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A200302 Decimal expansion of greatest x satisfying 4*x^2 - 3*cos(x) = 3*sin(x).

%I A200302 #12 Feb 12 2025 14:36:14
%S A200302 1,0,1,6,1,4,3,9,5,6,7,2,3,5,5,8,7,3,3,7,9,9,4,5,5,9,0,1,2,9,6,8,6,4,
%T A200302 7,4,6,8,7,7,9,9,4,9,2,5,9,9,2,1,9,8,1,9,8,1,9,0,3,6,6,3,3,4,1,4,8,1,
%U A200302 0,7,6,3,7,0,8,3,4,4,0,9,5,0,4,4,0,1,3,4,3,9,8,5,6,2,0,2,9,6,9
%N A200302 Decimal expansion of greatest x satisfying 4*x^2 - 3*cos(x) = 3*sin(x).
%C A200302 See A199949 for a guide to related sequences. The Mathematica program includes a graph.
%H A200302 G. C. Greubel, <a href="/A200302/b200302.txt">Table of n, a(n) for n = 1..10000</a>
%H A200302 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A200302 least x: -0.52377415675325572171784049673944...
%e A200302 greatest x: 1.016143956723558733799455901296...
%t A200302 a = 4; b = -3; c = 3;
%t A200302 f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
%t A200302 Plot[{f[x], g[x]}, {x, -1, 1}, {AxesOrigin -> {0, 0}}]
%t A200302 r = x /. FindRoot[f[x] == g[x], {x, -.54, -.51}, WorkingPrecision -> 110]
%t A200302 RealDigits[r]   (* A200297 *)
%t A200302 r = x /. FindRoot[f[x] == g[x], {x, 1, 1.05}, WorkingPrecision -> 110]
%t A200302 RealDigits[r]   (* A200298 *)
%o A200302 (PARI) a=4; b=-3; c=3; solve(x=1, 2, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jul 08 2018
%Y A200302 Cf. A199949.
%K A200302 nonn,cons
%O A200302 1,4
%A A200302 _Clark Kimberling_, Nov 15 2011