cp's OEIS Frontend

A197011 Decimal expansion of the slope of the line y=mx which meets the curve y=cos(x+1/2) orthogonally over the interval [0, 2*Pi] (as in A197010).

%I A197011 #8 Apr 10 2021 02:04:30
%S A197011 1,2,1,4,5,5,6,2,7,2,0,0,1,0,5,6,9,8,0,2,9,9,8,8,0,1,6,7,5,4,7,7,7,7,
%T A197011 6,2,0,4,2,9,7,3,0,6,2,9,3,4,2,3,0,1,1,0,7,5,5,0,6,1,4,8,2,3,4,8,8,0,
%U A197011 8,3,4,2,2,5,6,0,8,4,2,7,4,5,6,0,0,6,6,7,4,8,5,3,8,8,8,6,5,7,1,9,7
%N A197011 Decimal expansion of the slope of the line y=mx which meets the curve y=cos(x+1/2) orthogonally over the interval [0, 2*Pi] (as in A197010).
%C A197011 See the Mathematica program for a graph.
%C A197011 xo=0.4672816053760121337816307268...
%C A197011 yo=0.5675398046001583628839615011...
%C A197011 m=1.21455627200105698029988016754...
%C A197011 |OP|=0.73515544514637791501789646...
%t A197011 c = 1/2;
%t A197011 xo = x /. FindRoot[x == Sin[x + c] Cos[x + c], {x, .8, 1.2}, WorkingPrecision -> 100]
%t A197011 RealDigits[xo] (* A197010 *)
%t A197011 m = 1/Sin[xo + c]
%t A197011 RealDigits[m]  (* A197011 *)
%t A197011 yo = m*xo
%t A197011 d = Sqrt[xo^2 + yo^2]
%t A197011 Show[Plot[{Cos[x + c], yo - (1/m) (x - xo)}, {x, -Pi/4, Pi/2}], ContourPlot[{y == m*x}, {x, 0, Pi}, {y, 0, 1}], PlotRange -> All,
%t A197011 AspectRatio -> Automatic, AxesOrigin -> Automatic]
%Y A197011 Cf. A197010, A197002, A196996, A197000.
%K A197011 nonn,cons
%O A197011 1,2
%A A197011 _Clark Kimberling_, Oct 10 2011