A197007 - OEIS

%I #8 Apr 10 2021 02:04:37

%S 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 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 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 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 See the Mathematica program for a graph.

%C xo=0.460885580860965976987981282513698...

%C yo=0.553292712300593256734925495541442...

%C m=1.2004990723879979061250465124427113...

%C |OP|=0.7201030093885853693640956082816...

%t c = Pi/6;

%t xo = x /.  FindRoot[x == Sin[x + c] Cos[x + c], {x, .8, 1.2}, WorkingPrecision -> 100]

%t RealDigits[xo] (* A197006 *)

%t m = 1/Sin[xo + c]

%t RealDigits[m] (* A197007 *)

%t yo = m*xo

%t d = Sqrt[xo^2 + yo^2]

%t 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 AspectRatio -> Automatic, AxesOrigin -> Automatic]

%Y Cf. A197006, A197002, A196996, A197000.

%K nonn,cons

%O 1,2

%A _Clark Kimberling_, Oct 10 2011