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A197006 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/6) orthogonally.

%I A197006 #8 Apr 10 2021 02:04:41
%S A197006 4,6,0,8,8,5,5,8,0,8,6,0,9,6,5,9,7,6,9,8,7,9,8,1,2,8,2,5,1,3,6,9,8,2,
%T A197006 7,7,2,4,3,7,4,9,9,9,8,7,4,3,9,3,4,3,5,6,9,3,2,5,7,8,4,3,3,9,2,4,8,3,
%U A197006 4,7,5,2,2,8,8,0,3,8,7,9,7,1,3,0,5,0,5,9,7,4,8,0,7,6,7,9,4,3,8,4
%N A197006 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/6) orthogonally.
%C A197006 See the Mathematica program for a graph.
%C A197006 xo=0.460885580860965976987981282513698...
%C A197006 yo=0.553292712300593256734925495541442...
%C A197006 m=1.2004990723879979061250465124427113...
%C A197006 |OP|=0.7201030093885853693640956082816...
%t A197006 c = Pi/6;
%t A197006 xo = x /.  FindRoot[x == Sin[x + c] Cos[x + c], {x, .8, 1.2}, WorkingPrecision -> 100]
%t A197006 RealDigits[xo] (* A197006 *)
%t A197006 m = 1/Sin[xo + c]
%t A197006 RealDigits[m] (* A197007 *)
%t A197006 yo = m*xo
%t A197006 d = Sqrt[xo^2 + yo^2]
%t A197006 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 A197006 AspectRatio -> Automatic, AxesOrigin -> Automatic]
%Y A197006 Cf. A197007, A197002, A196996, A197000.
%K A197006 nonn,cons
%O A197006 0,1
%A A197006 _Clark Kimberling_, Oct 10 2011