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

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

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

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

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

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

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

%e x=0.773981117427467177521657303986725303016750...

%t a = 3; b = -2; c = 1;

%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, .77, .78}, WorkingPrecision -> 110]

%t RealDigits[r] (* A199508 *)

%Y Cf. A199429.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Nov 07 2011