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A200109 Decimal expansion of least x satisfying 2*x^2 - cos(x) = 2*sin(x), negated.

%I A200109 #11 Feb 12 2025 09:55:28
%S A200109 3,5,2,3,6,5,0,0,5,7,7,7,3,2,6,4,5,3,1,0,2,8,6,6,1,9,5,3,5,9,9,9,6,8,
%T A200109 1,0,8,6,8,5,9,0,3,3,1,2,4,3,7,1,6,9,7,9,3,6,0,2,5,2,5,0,3,8,5,6,6,5,
%U A200109 7,4,5,4,2,5,4,0,3,3,6,7,0,3,7,7,7,9,1,1,0,6,1,4,3,6,9,5,9,4,6
%N A200109 Decimal expansion of least x satisfying 2*x^2 - cos(x) = 2*sin(x), negated.
%C A200109 See A199949 for a guide to related sequences. The Mathematica program includes a graph.
%H A200109 G. C. Greubel, <a href="/A200109/b200109.txt">Table of n, a(n) for n = 0..10000</a>
%H A200109 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A200109 least x: -0.35236500577732645310286619535999...
%e A200109 greatest x: 1.056698376942878122192408303117...
%t A200109 a = 2; b = -1; c = 2;
%t A200109 f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
%t A200109 Plot[{f[x], g[x]}, {x, -3, 3}, {AxesOrigin -> {0, 0}}]
%t A200109 r = x /. FindRoot[f[x] == g[x], {x, -.36, -.35}, WorkingPrecision -> 110]
%t A200109 RealDigits[r]  (* A200109 *)
%t A200109 r = x /. FindRoot[f[x] == g[x], {x, 1.05, 1.06}, WorkingPrecision -> 110]
%t A200109 RealDigits[r]  (* A200110 *)
%o A200109 (PARI) a=2; b=-1; c=2; solve(x=-1, 0, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jun 25 2018
%Y A200109 Cf. A199949.
%K A200109 nonn,cons
%O A200109 0,1
%A A200109 _Clark Kimberling_, Nov 13 2011