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A199958 Decimal expansion of greatest x satisfying x^2 + 2*cos(x) = 4*sin(x).

%I A199958 #12 Feb 08 2025 23:04:02
%S A199958 2,1,1,1,5,9,4,8,6,7,3,1,3,0,9,4,1,6,6,6,4,6,4,1,3,3,1,0,9,9,2,0,7,4,
%T A199958 5,4,6,0,6,7,6,8,3,5,7,6,1,4,3,6,4,6,4,5,3,4,0,0,6,1,8,8,8,3,7,3,2,8,
%U A199958 4,5,1,2,2,9,1,7,9,0,0,3,6,6,6,5,8,1,5,8,8,3,6,6,7,2,6,2,4,9,1
%N A199958 Decimal expansion of greatest x satisfying x^2 + 2*cos(x) = 4*sin(x).
%C A199958 See A199949 for a guide to related sequences. The Mathematica program includes a graph.
%H A199958 G. C. Greubel, <a href="/A199958/b199958.txt">Table of n, a(n) for n = 1..10000</a>
%H A199958 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A199958 least x:  0.525416279282353649071522053392...
%e A199958 greatest x: 2.1115948673130941666464133109...
%t A199958 a = 1; b = 2; c = 4;
%t A199958 f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
%t A199958 Plot[{f[x], g[x]}, {x, -1, 3}, {AxesOrigin -> {0, 0}}]
%t A199958 r = x /. FindRoot[f[x] == g[x], {x, .52, .53}, WorkingPrecision -> 110]
%t A199958 RealDigits[r]  (* A199957 *)
%t A199958 r = x /. FindRoot[f[x] == g[x], {x, 2.1, 2.2}, WorkingPrecision -> 110]
%t A199958 RealDigits[r]  (* A199958 *)
%o A199958 (PARI) a=1; b=2; c=4; solve(x=0, 1, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jun 22 2018
%Y A199958 Cf. A199949.
%K A199958 nonn,cons
%O A199958 1,1
%A A199958 _Clark Kimberling_, Nov 12 2011