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%I A196996 #7 Mar 30 2012 18:57:50
%S A196996 9,3,5,0,2,7,2,8,8,4,7,4,9,6,7,8,3,6,1,4,5,1,9,4,4,2,7,5,3,2,3,9,7,7,
%T A196996 6,3,1,7,5,1,8,3,5,1,0,0,5,2,6,8,3,9,0,8,9,5,3,4,7,2,9,7,9,7,0,1,2,8,
%U A196996 5,7,1,3,0,3,2,2,9,6,3,6,0,2,7,4,7,3,1,0,4,9,2,9,1,6,2,8,9,9,9,4
%N A196996 Decimal expansion of xo, where P=(xo,yo) is the point nearest O=(0,0) at which a line y=m*x meets the curve y=cos(3x) orthogonally.
%C A196996 See the Mathematica program for a graph.
%C A196996 xo=0.9350272884749678361451944275323...
%C A196996 yo=0.3301955980451199836007253971727...
%C A196996 m=0.35314006565912096755666111412785...
%C A196996 |OP|=0.99161744799152518925689622748...
%t A196996 c = 3;
%t A196996 xo = x /. FindRoot[0 == x + c*Sin[c*x] Cos[c*x], {x, .8, 1.2}, WorkingPrecision -> 100]
%t A196996 RealDigits[xo] (* A196996 *)
%t A196996 m = Sin[c*xo]/xo
%t A196996 RealDigits[m]  (* A196997 *)
%t A196996 yo = m*xo
%t A196996 d = Sqrt[xo^2 + yo^2]
%t A196996 Show[Plot[{Sin[c*x], yo - (1/m) (x - xo)}, {x, 0, Pi/c}], ContourPlot[{y == m*x}, {x, 0, 1.5}, {y, -.1, 1}], PlotRange -> All, AspectRatio -> Automatic]
%Y A196996 Cf. A196997, A197000, A197002.
%K A196996 nonn,cons
%O A196996 0,1
%A A196996 _Clark Kimberling_, Oct 09 2011

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