%I #9 May 13 2013 01:49:59

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

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

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

%N Decimal expansion of x>0 satisfying 2*x^2 - 2*x*cos(x) = 3*sin(x).

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

%e 1.331486959335040503327363069917339543025...

%t a = 2; b = -2; c = 3;

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

%t Plot[{f[x], g[x]}, {x, -1, 2}, {AxesOrigin -> {0, 0}}]

%t r = x /. FindRoot[f[x] == g[x], {x, 1.33, 1.34}, WorkingPrecision -> 110]

%t RealDigits[r] (* A199775 *)

%o (PARI) solve(x=1,2,2*x^2-2*x*cos(x)-3*sin(x)) \\ _Charles R Greathouse IV_, Dec 28 2011

%Y Cf. A199597.

%K nonn,cons

%O 1,2

%A _Clark Kimberling_, Nov 10 2011