%I #5 Mar 30 2012 18:57:58

%S 3,4,5,2,8,9,9,8,8,8,5,3,2,9,2,7,7,8,0,3,3,6,3,0,0,8,3,7,8,6,4,9,8,3,

%T 8,8,4,0,8,8,3,6,8,5,5,6,5,7,8,5,1,5,3,8,6,4,0,5,6,2,7,2,9,0,9,5,5,1,

%U 8,5,6,4,0,8,5,9,2,4,4,5,4,6,8,3,0,5,7,0,2,5,8,4,9,8,6,0,9,6,0

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

%C See A199597 for a guide to related sequences. The Mathematica program includes a graph.

%e least: 0.80005334262741575936859027990893321963...

%e greatest: 3.4528998885329277803363008378649838...

%t a = 1; b = 4; c = 4;

%t f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c*Sin[x]

%t Plot[{f[x], g[x]}, {x, -.5, 4}, {AxesOrigin -> {0, 0}}]

%t r = x /. FindRoot[f[x] == g[x], {x, .8, .81}, WorkingPrecision -> 110]

%t RealDigits[r] (* A199619, least pos root *)

%t r = x /. FindRoot[f[x] == g[x], {x, 3.4, 3.5}, WorkingPrecision -> 110]

%t RealDigits[r] (* A199620, greatest of 3 roots *)

%Y Cf. A199597.

%K nonn,cons

%O 1,1

%A _Clark Kimberling_, Nov 08 2011