cp's OEIS Frontend

A197004 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+Pi/3) orthogonally.

%I A197004 #8 Apr 10 2021 02:04:49
%S A197004 2,5,5,4,6,5,2,8,6,1,0,3,8,5,3,5,9,6,6,9,5,8,8,2,6,9,6,6,1,3,3,2,0,2,
%T A197004 7,2,6,5,4,7,8,8,3,5,5,9,5,3,7,0,8,5,2,8,9,3,0,2,5,2,6,7,6,7,2,9,7,6,
%U A197004 4,8,2,2,6,7,0,9,3,0,6,6,8,2,5,0,6,4,1,1,1,8,3,6,7,2,5,8,9,1,1,4
%N A197004 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+Pi/3) orthogonally.
%C A197004 See the Mathematica program for a graph.
%C A197004 xo=0.255465286103853596695882696613320272654788...
%C A197004 yo=0.264932084602776862434116494762571068650190...
%C A197004 m=1.0370570837365150046614795837584277605222343...
%C A197004 |OP|=0.3680373919265496189530095416155881110455...
%t A197004 c = Pi/3;
%t A197004 xo = x /. FindRoot[x == Sin[x + c] Cos[x + c], {x, .8, 1.2}, WorkingPrecision -> 100]
%t A197004 RealDigits[xo] (* A197004 *)
%t A197004 m = 1/Sin[xo + c]
%t A197004 RealDigits[m]  (* A197005 *)
%t A197004 yo = m*xo
%t A197004 d = Sqrt[xo^2 + yo^2]
%t A197004 Show[Plot[{Cos[x + c], yo - (1/m) (x - xo)}, {x, -Pi/4, Pi/2}],
%t A197004 ContourPlot[{y == m*x}, {x, 0, Pi}, {y, 0, 1}], PlotRange -> All,
%t A197004 AspectRatio -> Automatic, AxesOrigin -> Automatic]
%Y A197004 Cf. A197002, A196996, A197000.
%K A197004 nonn,cons
%O A197004 0,1
%A A197004 _Clark Kimberling_, Oct 10 2011