cp's OEIS Frontend

A197010 Decimal expansion of xo, where P=(xo,yo) is the point nearest O=(0,0) in which a line y=mx meets the curve y=cos(x+1/2) orthogonally.

%I A197010 #5 Mar 30 2012 18:57:50
%S A197010 4,6,7,2,8,1,6,0,5,3,7,6,0,1,2,1,3,3,7,8,1,6,3,0,7,2,6,8,8,4,4,2,5,0,
%T A197010 1,3,8,1,1,6,5,1,4,2,4,6,7,6,6,7,0,6,4,5,1,6,4,1,1,5,8,9,7,7,7,0,6,7,
%U A197010 5,6,3,4,7,2,2,9,6,3,6,4,1,5,5,0,3,8,9,3,6,1,1,6,6,2,0,5,3,7,2,2
%N A197010 Decimal expansion of xo, where P=(xo,yo) is the point nearest O=(0,0) in which a line y=mx meets the curve y=cos(x+1/2) orthogonally.
%C A197010 See the Mathematica program for a graph.
%C A197010 xo=0.4672816053760121337816307268...
%C A197010 yo=0.5675398046001583628839615011...
%C A197010 m=1.21455627200105698029988016754...
%C A197010 |OP|=0.73515544514637791501789646...
%t A197010 c = 1/2;
%t A197010 xo = x /. FindRoot[x == Sin[x + c] Cos[x + c], {x, .8, 1.2}, WorkingPrecision -> 100]
%t A197010 RealDigits[xo] (* A197010 *)
%t A197010 m = 1/Sin[xo + c]
%t A197010 RealDigits[m]  (* A197011 *)
%t A197010 yo = m*xo
%t A197010 d = Sqrt[xo^2 + yo^2]
%t A197010 Show[Plot[{Cos[x + c], yo - (1/m) (x - xo)}, {x, -Pi/4, Pi/2}],
%t A197010  ContourPlot[{y == m*x}, {x, 0, Pi}, {y, 0, 1}], PlotRange -> All,
%t A197010  AspectRatio -> Automatic, AxesOrigin -> Automatic]
%Y A197010 Cf. A179378, A197011, A197002, A196996, A197000.
%K A197010 nonn,cons
%O A197010 0,1
%A A197010 _Clark Kimberling_, Oct 10 2011