cp's OEIS Frontend

A196999 Decimal expansion of slope of the line y=mx which meets the curve y=cos(5x/2) orthogonally (as in A196998).

%I A196999 #5 Mar 30 2012 18:57:50
%S A196999 4,5,6,4,8,5,0,4,2,0,2,3,4,5,0,1,2,8,1,3,9,7,6,0,6,4,7,4,3,5,4,1,3,7,
%T A196999 1,7,0,6,4,3,0,5,0,9,2,7,8,2,9,2,8,5,3,8,2,3,5,8,0,0,3,1,8,0,1,9,6,2,
%U A196999 6,6,6,0,4,8,0,0,6,8,5,3,6,2,8,1,6,8,7,0,7,7,1,2,8,6,7,3,1,0,8
%N A196999 Decimal expansion of slope of the line y=mx which meets the curve y=cos(5x/2) orthogonally (as in A196998).
%C A196999 See the Mathematica program for a graph.
%C A196999 xo=1.055537135075475249854148417892290354122...
%C A196999 yo=0.481836913462240473673427172075977637742...
%C A196999 m=0.4564850420234501281397606474354137170643...
%C A196999 |OP|=1.1603126538559168441096914160911620183...
%t A196999 c = 5/2;
%t A196999 xo = x /.  FindRoot[0 == x + c*Sin[c*x] Cos[c*x], {x, .8, 1.2}, WorkingPrecision -> 100]
%t A196999 RealDigits[xo] (* A196998 *)
%t A196999 m = Sin[c*xo]/xo
%t A196999 RealDigits[m]  (* A196999 *)
%t A196999 yo = m*xo
%t A196999 d = Sqrt[xo^2 + yo^2]
%t A196999 Show[Plot[{Sin[c*x], yo - (1/m) (x - xo)}, {x, 0, Pi/c}],
%t A196999  ContourPlot[{y == m*x}, {x, 0, Pi/c}, {y, -.1, 1}], PlotRange -> All, AspectRatio -> Automatic]
%Y A196999 Cf. A196996, A196997, A197000, A197002.
%K A196999 nonn,cons
%O A196999 0,1
%A A196999 _Clark Kimberling_, Oct 09 2011