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A199957 Decimal expansion of least x satisfying x^2 + 2*cos(x) = 4*sin(x).

%I A199957 #12 Feb 08 2025 23:03:56
%S A199957 5,2,5,4,1,6,2,7,9,2,8,2,3,5,3,6,4,9,0,7,1,5,2,2,0,5,3,3,9,2,6,8,9,6,
%T A199957 5,6,7,3,8,8,5,6,5,3,0,2,0,7,8,3,2,8,4,4,6,3,6,0,9,8,3,8,0,6,7,2,5,4,
%U A199957 7,6,7,6,6,0,7,4,2,3,4,8,8,5,3,7,0,6,4,8,5,2,4,7,7,1,1,8,8,6,8
%N A199957 Decimal expansion of least x satisfying x^2 + 2*cos(x) = 4*sin(x).
%C A199957 See A199949 for a guide to related sequences. The Mathematica program includes a graph.
%H A199957 G. C. Greubel, <a href="/A199957/b199957.txt">Table of n, a(n) for n = 0..10000</a>
%H A199957 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A199957 least x:  0.525416279282353649071522053392...
%e A199957 greatest x: 2.1115948673130941666464133109...
%t A199957 a = 1; b = 2; c = 4;
%t A199957 f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
%t A199957 Plot[{f[x], g[x]}, {x, -1, 3}, {AxesOrigin -> {0, 0}}]
%t A199957 r = x /. FindRoot[f[x] == g[x], {x, .52, .53}, WorkingPrecision -> 110]
%t A199957 RealDigits[r]   (* A199957 *)
%t A199957 r = x /. FindRoot[f[x] == g[x], {x, 2.1, 2.2}, WorkingPrecision -> 110]
%t A199957 RealDigits[r]  (* A199958 *)
%o A199957 (PARI) a=1; b=2; c=4; solve(x=.5, 1, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jun 22 2018
%Y A199957 Cf. A199949.
%K A199957 nonn,cons
%O A199957 0,1
%A A199957 _Clark Kimberling_, Nov 12 2011