cp's OEIS Frontend

A197005 Decimal expansion of the slope of the line y=mx which meets the curve y=cos(x+Pi/3) orthogonally over the interval [0, 2*Pi] (as in A197004).

%I A197005 #8 Apr 10 2021 02:04:46
%S A197005 1,0,3,7,0,5,7,0,8,3,7,3,6,5,1,5,0,0,4,6,6,1,4,7,9,5,8,3,7,5,8,4,2,7,
%T A197005 7,6,0,5,2,2,2,3,4,3,4,3,1,3,9,2,5,1,5,3,1,6,5,5,2,9,5,2,4,2,0,6,8,4,
%U A197005 8,7,9,8,7,2,3,9,7,5,1,8,7,8,7,4,8,1,7,2,3,2,2,4,5,5,9,3,3,2,8,0,8,9
%N A197005 Decimal expansion of the slope of the line y=mx which meets the curve y=cos(x+Pi/3) orthogonally over the interval [0, 2*Pi] (as in A197004).
%C A197005 See the Mathematica program for a graph.
%C A197005 xo=0.255465286103853596695882696613320272654788...
%C A197005 yo=0.264932084602776862434116494762571068650190...
%C A197005 m=1.0370570837365150046614795837584277605222343...
%C A197005 |OP|=0.3680373919265496189530095416155881110455...
%t A197005 c = Pi/3;
%t A197005 xo = x /.  FindRoot[x == Sin[x + c] Cos[x + c], {x, .8, 1.2}, WorkingPrecision -> 100]
%t A197005 RealDigits[xo] (* A197004 *)
%t A197005 m = 1/Sin[xo + c]
%t A197005 RealDigits[m]  (* A197005 *)
%t A197005 yo = m*xo
%t A197005 d = Sqrt[xo^2 + yo^2]
%t A197005 Show[Plot[{Cos[x + c], yo - (1/m) (x - xo)}, {x, -Pi/4, Pi/2}],
%t A197005 ContourPlot[{y == m*x}, {x, 0, Pi}, {y, 0, 1}], PlotRange -> All,
%t A197005 AspectRatio -> Automatic, AxesOrigin -> Automatic]
%Y A197005 Cf. A197004, A197002, A196996, A197000.
%K A197005 nonn,cons
%O A197005 1,3
%A A197005 _Clark Kimberling_, Oct 10 2011