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A196998 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(5x/2) orthogonally.

%I A196998 #5 Mar 30 2012 18:57:50
%S A196998 1,0,5,5,5,3,7,1,3,5,0,7,5,4,7,5,2,4,9,8,5,4,1,4,8,4,1,7,8,9,2,2,9,0,
%T A196998 3,5,4,1,2,2,2,7,9,8,0,6,9,6,2,7,3,2,9,7,3,0,4,0,0,8,2,4,1,7,5,4,1,5,
%U A196998 4,5,5,4,2,8,0,0,9,4,4,9,3,6,6,6,9,4,4,5,9,1,5,5,0,4,5,7,4,7,1,5
%N A196998 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(5x/2) orthogonally.
%C A196998 See the Mathematica program for a graph.
%C A196998 xo=1.055537135075475249854148417892290354122...
%C A196998 yo=0.481836913462240473673427172075977637742...
%C A196998 m=0.4564850420234501281397606474354137170643...
%C A196998 |OP|=1.1603126538559168441096914160911620183...
%t A196998 c = 5/2;
%t A196998 xo = x /.  FindRoot[0 == x + c*Sin[c*x] Cos[c*x], {x, .8, 1.2}, WorkingPrecision -> 100]
%t A196998 RealDigits[xo] (* A196998 *)
%t A196998 m = Sin[c*xo]/xo
%t A196998 RealDigits[m]  (* A196999 *)
%t A196998 yo = m*xo
%t A196998 d = Sqrt[xo^2 + yo^2]
%t A196998 Show[Plot[{Sin[c*x], yo - (1/m) (x - xo)}, {x, 0, Pi/c}],
%t A196998  ContourPlot[{y == m*x}, {x, 0, Pi/c}, {y, -.1, 1}], PlotRange -> All, AspectRatio -> Automatic]
%Y A196998 Cf. A196996, A197000, A197002.
%K A196998 nonn,cons
%O A196998 1,3
%A A196998 _Clark Kimberling_, Oct 09 2011