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

%I #8 Mar 30 2012 18:57:57

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

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

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

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

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

%e x=1.3299032684690480269887796580804060825373320...

%t a = 1; b = -1; 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, 1.32, 1.33}, WorkingPrecision -> 110]

%t RealDigits[r] (* A199455 *)

%Y Cf. A199429.

%K nonn,cons

%O 1,2

%A _Clark Kimberling_, Nov 06 2011