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A200124 Decimal expansion of least x satisfying 2*x^2 - 3*cos(x) = 3*sin(x), negated.

%I A200124 #12 Feb 12 2025 13:00:02
%S A200124 6,0,9,4,1,6,8,3,3,2,6,3,2,7,5,2,9,9,9,3,0,7,5,3,5,9,9,3,1,6,0,5,4,8,
%T A200124 2,2,7,8,5,2,3,3,0,3,0,5,9,3,5,8,3,5,5,5,9,6,0,5,1,3,3,4,7,1,7,8,1,7,
%U A200124 1,9,6,0,4,8,7,5,2,6,3,9,0,1,3,4,2,5,3,7,1,3,4,8,5,4,4,5,6,0,3
%N A200124 Decimal expansion of least x satisfying 2*x^2 - 3*cos(x) = 3*sin(x), negated.
%C A200124 See A199949 for a guide to related sequences. The Mathematica program includes a graph.
%H A200124 G. C. Greubel, <a href="/A200124/b200124.txt">Table of n, a(n) for n = 0..10000</a>
%H A200124 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A200124 least x: -0.6094168332632752999307535993160...
%e A200124 greatest x: 1.34204053424075776611980105081...
%t A200124 a = 2; b = -3; c = 3;
%t A200124 f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
%t A200124 Plot[{f[x], g[x]}, {x, -3, 3}, {AxesOrigin -> {0, 0}}]
%t A200124 r = x /. FindRoot[f[x] == g[x], {x, -.61, -.60}, WorkingPrecision -> 110]
%t A200124 RealDigits[r]  (* A200124 *)
%t A200124 r = x /. FindRoot[f[x] == g[x], {x, 1.34, 1.35}, WorkingPrecision -> 110]
%t A200124 RealDigits[r]  (* A200125 *)
%o A200124 (PARI) a=2; b=-3; c=3; solve(x=-1, 0, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jul 01 2018
%Y A200124 Cf. A199949.
%K A200124 nonn,cons
%O A200124 0,1
%A A200124 _Clark Kimberling_, Nov 14 2011