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

%I #5 Mar 30 2012 18:57:58

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

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

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

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

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

%e x=0.9922917949161176981841193385017574750...

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

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

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

%t r = x /. FindRoot[f[x] == g[x], {x, .99, 1}, WorkingPrecision -> 110]

%t RealDigits[r] (* A199623 *)

%Y Cf. A199597.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Nov 08 2011