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A200095 Decimal expansion of least x satisfying x^2 - 3*cos(x) = 3*sin(x), negated.

%I A200095 #13 Feb 12 2025 09:53:22
%S A200095 6,7,7,1,1,9,4,1,1,6,9,7,9,4,3,1,3,0,1,8,4,1,7,9,5,2,0,0,9,8,9,1,7,0,
%T A200095 2,1,5,5,6,6,4,5,5,5,2,5,3,3,6,9,3,2,4,4,3,7,6,9,1,1,5,4,0,1,8,3,5,0,
%U A200095 3,8,3,8,7,6,2,7,8,4,0,3,8,9,9,8,9,8,2,7,3,9,2,3,4,8,4,8,2,9,5
%N A200095 Decimal expansion of least x satisfying x^2 - 3*cos(x) = 3*sin(x), negated.
%C A200095 See A199949 for a guide to related sequences. The Mathematica program includes a graph.
%H A200095 G. C. Greubel, <a href="/A200095/b200095.txt">Table of n, a(n) for n = 0..10000</a>
%H A200095 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A200095 least x:  -0.677119411697943130184179520098917021...
%e A200095 greatest x: 1.6546997822939010711316866818308006354...
%t A200095 a = 1; b = -3; c = 3;
%t A200095 f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
%t A200095 Plot[{f[x], g[x]}, {x, -3, 3}, {AxesOrigin -> {0, 0}}]
%t A200095 r = x /. FindRoot[f[x] == g[x], {x, -.88, -.67}, WorkingPrecision -> 110]
%t A200095 RealDigits[r]  (* A200095 *)
%t A200095 r = x /. FindRoot[f[x] == g[x], {x, 1.65, 1.66}, WorkingPrecision -> 110]
%t A200095 RealDigits[r]  (* A200096 *)
%o A200095 (PARI) a=1; b=-3; c=3; solve(x=-1, 0, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jun 24 2018
%Y A200095 Cf. A199949.
%K A200095 nonn,cons
%O A200095 0,1
%A A200095 _Clark Kimberling_, Nov 13 2011