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

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

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

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

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

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

%C See A199370 for a guide to related sequences. The Mathematica program includes a graph.

%e x=0.477947554121687356519723345940414530738979582349442...

%t a = 1; b = 3; 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, .47, .48}, WorkingPrecision -> 110]

%t RealDigits[r] (* A199435 *)

%Y Cf. A199429.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Nov 06 2011