cp's OEIS Frontend

A197007 Decimal expansion of the slope of the line y=mx which meets the curve y=cos(x+Pi/6) orthogonally over the interval [0, 2*Pi] (as in A197006).

%I A197007 #8 Apr 10 2021 02:04:37
%S A197007 1,2,0,0,4,9,9,0,7,2,3,8,7,9,9,7,9,0,6,1,2,5,0,4,6,5,1,2,4,4,2,7,1,1,
%T A197007 3,4,2,4,3,7,6,8,0,1,7,5,1,3,2,9,9,4,0,6,8,6,6,0,5,0,4,2,1,9,0,9,4,4,
%U A197007 4,7,6,1,0,3,8,1,3,6,2,4,2,6,8,5,5,6,4,8,5,6,0,5,1,1,4,3,3,6,6,3,6
%N A197007 Decimal expansion of the slope of the line y=mx which meets the curve y=cos(x+Pi/6) orthogonally over the interval [0, 2*Pi] (as in A197006).
%C A197007 See the Mathematica program for a graph.
%C A197007 xo=0.460885580860965976987981282513698...
%C A197007 yo=0.553292712300593256734925495541442...
%C A197007 m=1.2004990723879979061250465124427113...
%C A197007 |OP|=0.7201030093885853693640956082816...
%t A197007 c = Pi/6;
%t A197007 xo = x /.  FindRoot[x == Sin[x + c] Cos[x + c], {x, .8, 1.2}, WorkingPrecision -> 100]
%t A197007 RealDigits[xo] (* A197006 *)
%t A197007 m = 1/Sin[xo + c]
%t A197007 RealDigits[m] (* A197007 *)
%t A197007 yo = m*xo
%t A197007 d = Sqrt[xo^2 + yo^2]
%t A197007 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 A197007 AspectRatio -> Automatic, AxesOrigin -> Automatic]
%Y A197007 Cf. A197006, A197002, A196996, A197000.
%K A197007 nonn,cons
%O A197007 1,2
%A A197007 _Clark Kimberling_, Oct 10 2011