A199462 - OEIS

%I #6 Mar 30 2012 18:57:57

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

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

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

%N Decimal expansion of x>0 satisfying x^2-2*x*sin(x)=2*cos(x).

%C See A199429 for a guide to related sequences.  The Mathematica program includes a graph.

%e x=1.7560266924597034329425334892642392358108127...

%t a = 1; b = -2; c = 2;

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

%t Plot[{f[x], g[x]}, {x, -Pi, Pi}, {AxesOrigin -> {0, 0}}]

%t r = x /. FindRoot[f[x] == g[x], {x, 1.75, 1.76}, WorkingPrecision -> 110]

%t RealDigits[r]  (* A199462 *)

%Y Cf. A199429.

%K nonn,cons

%O 1,2

%A _Clark Kimberling_, Nov 07 2011