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A200125 Decimal expansion of greatest x satisfying 2*x^2 - 3*cos(x) = 3*sin(x).

%I A200125 #12 Feb 12 2025 13:00:22
%S A200125 1,3,4,2,0,4,0,5,3,4,2,4,0,7,5,7,7,6,6,1,1,9,8,0,1,0,5,0,8,1,8,2,3,8,
%T A200125 9,7,1,5,9,4,9,8,2,7,1,6,0,4,4,0,1,0,4,7,2,7,2,0,7,8,0,9,4,5,4,1,7,3,
%U A200125 8,6,6,9,8,0,8,6,7,8,7,4,1,4,5,7,1,3,9,4,4,1,3,4,0,8,7,5,0,9,7
%N A200125 Decimal expansion of greatest x satisfying 2*x^2 - 3*cos(x) = 3*sin(x).
%C A200125 See A199949 for a guide to related sequences. The Mathematica program includes a graph.
%H A200125 G. C. Greubel, <a href="/A200125/b200125.txt">Table of n, a(n) for n = 1..10000</a>
%H A200125 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A200125 least x: -0.6094168332632752999307535993160...
%e A200125 greatest x: 1.34204053424075776611980105081...
%t A200125 a = 2; b = -3; c = 3;
%t A200125 f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
%t A200125 Plot[{f[x], g[x]}, {x, -3, 3}, {AxesOrigin -> {0, 0}}]
%t A200125 r = x /. FindRoot[f[x] == g[x], {x, -.61, -.60}, WorkingPrecision -> 110]
%t A200125 RealDigits[r]  (* A200124 *)
%t A200125 r = x /. FindRoot[f[x] == g[x], {x, 1.34, 1.35}, WorkingPrecision -> 110]
%t A200125 RealDigits[r]  (* A200125 *)
%o A200125 (PARI) a=2; b=-3; c=3; solve(x=1, 2, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jul 01 2018
%Y A200125 Cf. A199949.
%K A200125 nonn,cons
%O A200125 1,2
%A A200125 _Clark Kimberling_, Nov 14 2011