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A200103 Decimal expansion of least x satisfying x^2 - 4*cos(x) = 3*sin(x), negated.

%I A200103 #11 Feb 12 2025 09:54:25
%S A200103 7,9,9,2,0,0,8,1,6,8,9,5,0,9,7,0,0,5,9,4,4,4,6,0,0,6,9,2,3,2,1,1,0,1,
%T A200103 0,4,1,2,5,1,2,1,2,6,7,1,1,1,6,1,4,3,6,3,7,8,0,2,0,8,4,8,6,9,4,0,5,8,
%U A200103 0,2,7,0,8,4,8,0,7,3,4,1,6,4,1,1,8,9,1,8,7,8,2,4,3,0,4,5,4,2,1
%N A200103 Decimal expansion of least x satisfying x^2 - 4*cos(x) = 3*sin(x), negated.
%C A200103 See A199949 for a guide to related sequences. The Mathematica program includes a graph.
%H A200103 G. C. Greubel, <a href="/A200103/b200103.txt">Table of n, a(n) for n = 0..10000</a>
%H A200103 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A200103 least x:  -0.79920081689509700594446006923211010...
%e A200103 greatest x: 1.643556567520171656906524761634888...
%t A200103 a = 1; b = -4; c = 3;
%t A200103 f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
%t A200103 Plot[{f[x], g[x]}, {x, -3, 3}, {AxesOrigin -> {0, 0}}]
%t A200103 r = x /. FindRoot[f[x] == g[x], {x, -.8, -.7}, WorkingPrecision -> 110]
%t A200103 RealDigits[r]  (* A200103 *)
%t A200103 r = x /. FindRoot[f[x] == g[x], {x, 1.64, 1.65}, WorkingPrecision -> 110]
%t A200103 RealDigits[r]  (* A200104 *)
%o A200103 (PARI) a=1; b=-4; c=3; solve(x=-1, 0, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jun 25 2018
%Y A200103 Cf. A199949.
%K A200103 nonn,cons
%O A200103 0,1
%A A200103 _Clark Kimberling_, Nov 13 2011