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A200093 Decimal expansion of least x satisfying x^2 - 3*cos(x) = 2*sin(x), negated.

%I A200093 #15 Feb 12 2025 09:53:19
%S A200093 8,0,2,9,9,2,1,5,4,2,9,7,8,8,4,2,5,0,7,2,0,3,3,5,4,5,3,4,7,4,8,7,1,2,
%T A200093 7,4,2,9,2,1,4,1,3,5,7,7,0,0,7,2,7,7,8,3,0,6,5,8,5,4,6,2,3,2,9,7,3,5,
%U A200093 2,1,2,9,9,1,4,3,9,4,2,5,5,9,3,6,6,4,9,4,1,0,6,9,9,2,0,4,1,7,7
%N A200093 Decimal expansion of least x satisfying x^2 - 3*cos(x) = 2*sin(x), negated.
%C A200093 See A199949 for a guide to related sequences. The Mathematica program includes a graph.
%H A200093 G. C. Greubel, <a href="/A200093/b200093.txt">Table of n, a(n) for n = 0..10000</a>
%H A200093 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A200093 least x:  -0.8029921542978842507203354534748712742...
%e A200093 greatest x: 1.492665923525132206969243059834936861...
%t A200093 a = 1; b = -3; c = 2;
%t A200093 f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
%t A200093 Plot[{f[x], g[x]}, {x, -2, 2}, {AxesOrigin -> {0, 0}}]
%t A200093 r = x /. FindRoot[f[x] == g[x], {x, -.81, -.80}, WorkingPrecision -> 110]
%t A200093 RealDigits[r]  (* A200093 *)
%t A200093 r = x /. FindRoot[f[x] == g[x], {x, 1.49, 1.50}, WorkingPrecision -> 110]
%t A200093 RealDigits[r]  (* A200094 *)
%o A200093 (PARI) a=1; b=-3; c=2; solve(x=-1, 0, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jun 24 2018
%Y A200093 Cf. A199949.
%K A200093 nonn,cons
%O A200093 0,1
%A A200093 _Clark Kimberling_, Nov 13 2011