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A200016 Decimal expansion of least x satisfying x^2 - cos(x) = 4*sin(x) (negated).

%I A200016 #18 Feb 12 2025 04:52:41
%S A200016 2,3,1,9,3,1,7,3,6,5,0,8,0,7,7,0,6,8,2,7,9,2,1,6,2,9,5,0,7,8,0,8,0,1,
%T A200016 1,5,5,2,8,9,5,6,6,7,4,9,1,7,6,0,4,6,3,1,5,8,1,2,1,7,4,2,7,6,4,9,1,9,
%U A200016 4,3,4,9,1,6,1,6,1,4,6,5,4,1,6,9,0,8,8,3,0,5,2,0,0,8,3,6,2,8,1
%N A200016 Decimal expansion of least x satisfying x^2 - cos(x) = 4*sin(x) (negated).
%C A200016 See A199949 for a guide to related sequences. The Mathematica program includes a graph.
%H A200016 G. C. Greubel, <a href="/A200016/b200016.txt">Table of n, a(n) for n = 0..10000</a>
%H A200016 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A200016 least x:  -0.231931736508077068279216295078080...
%e A200016 greatest x: 1.87520068875669013700099544270224...
%t A200016 a = 1; b = -1; c = 4;
%t A200016 f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
%t A200016 Plot[{f[x], g[x]}, {x, -1, 2}, {AxesOrigin -> {0, 0}}]
%t A200016 r = x /. FindRoot[f[x] == g[x], {x, -.24, -.23}, WorkingPrecision -> 110]
%t A200016 RealDigits[r]   (* A200016 *)
%t A200016 r = x /. FindRoot[f[x] == g[x], {x, 1.87, 1.88}, WorkingPrecision -> 110]
%t A200016 RealDigits[r]  (* A200017 *)
%o A200016 (PARI) a=1; b=-1; c=4; solve(x=-1, 0, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jun 24 2018
%Y A200016 Cf. A199949.
%K A200016 nonn,cons
%O A200016 0,1
%A A200016 _Clark Kimberling_, Nov 12 2011