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A200017 Decimal expansion of greatest x satisfying x^2 - cos(x) = 4*sin(x).

%I A200017 #11 Feb 12 2025 04:52:48
%S A200017 1,8,7,5,2,0,0,6,8,8,7,5,6,6,9,0,1,3,7,0,0,0,9,9,5,4,4,2,7,0,2,2,4,9,
%T A200017 1,3,9,1,5,1,8,7,1,7,6,0,4,2,4,5,7,9,4,7,0,6,9,5,5,6,0,1,4,9,5,6,5,1,
%U A200017 5,3,3,6,8,6,6,1,5,7,7,6,9,0,2,9,6,4,3,2,2,4,4,2,9,3,0,2,1,2,4
%N A200017 Decimal expansion of greatest x satisfying x^2 - cos(x) = 4*sin(x).
%C A200017 See A199949 for a guide to related sequences. The Mathematica program includes a graph.
%H A200017 G. C. Greubel, <a href="/A200017/b200017.txt">Table of n, a(n) for n = 1..10000</a>
%H A200017 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A200017 least x:  -0.231931736508077068279216295078080...
%e A200017 greatest x: 1.87520068875669013700099544270224...
%t A200017 a = 1; b = -1; c = 4;
%t A200017 f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
%t A200017 Plot[{f[x], g[x]}, {x, -1, 2}, {AxesOrigin -> {0, 0}}]
%t A200017 r = x /. FindRoot[f[x] == g[x], {x, -.24, -.23}, WorkingPrecision -> 110]
%t A200017 RealDigits[r]   (* A200016 *)
%t A200017 r = x /. FindRoot[f[x] == g[x], {x, 1.87, 1.88}, WorkingPrecision -> 110]
%t A200017 RealDigits[r]  (* A200017 *)
%o A200017 (PARI) a=1; b=-1; c=4; solve(x=1, 2, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jun 24 2018
%Y A200017 Cf. A199949.
%K A200017 nonn,cons
%O A200017 1,2
%A A200017 _Clark Kimberling_, Nov 12 2011