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A200130 Decimal expansion of least x satisfying 2*x^2 - 4*cos(x) = 3*sin(x), negated.

%I A200130 #12 Feb 12 2025 13:01:14
%S A200130 7,1,9,0,0,5,0,6,4,5,5,8,8,4,2,9,2,7,8,5,9,2,7,1,7,8,0,8,4,8,1,7,9,3,
%T A200130 8,2,5,0,1,8,8,0,5,3,7,6,4,8,4,5,9,1,3,3,2,1,2,0,0,9,5,6,6,5,6,9,8,1,
%U A200130 1,8,6,6,8,2,2,3,9,7,3,4,6,3,5,2,1,2,0,8,0,3,0,7,4,9,1,1,9,4,1
%N A200130 Decimal expansion of least x satisfying 2*x^2 - 4*cos(x) = 3*sin(x), negated.
%C A200130 See A199949 for a guide to related sequences. The Mathematica program includes a graph.
%H A200130 G. C. Greubel, <a href="/A200130/b200130.txt">Table of n, a(n) for n = 0..10000</a>
%H A200130 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A200130 least x: -0.71900506455884292785927178084817...
%e A200130 greatest x: 1.368149112042067667997699108890...
%t A200130 a = 2; b = -4; c = 3;
%t A200130 f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
%t A200130 Plot[{f[x], g[x]}, {x, -3, 3}, {AxesOrigin -> {0, 0}}]
%t A200130 r = x /. FindRoot[f[x] == g[x], {x, -.72, -.71}, WorkingPrecision -> 110]
%t A200130 RealDigits[r]  (* A200130 *)
%t A200130 r = x /. FindRoot[f[x] == g[x], {x, 1.36, 1.37}, WorkingPrecision -> 110]
%t A200130 RealDigits[r]  (* A200131 *)
%o A200130 (PARI) a=2; b=-4; c=3; solve(x=-1, 0, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jul 01 2018
%Y A200130 Cf. A199949.
%K A200130 nonn,cons
%O A200130 0,1
%A A200130 _Clark Kimberling_, Nov 14 2011