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.

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, 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, 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

Offset: 0

Author

Clark Kimberling, Oct 10 2011

Keywords

• nonn
• cons

Comments

See the Mathematica program for a graph.

xo=0.460885580860965976987981282513698...

yo=0.553292712300593256734925495541442...

m=1.2004990723879979061250465124427113...

|OP|=0.7201030093885853693640956082816...

Crossrefs

Cf. A197007, A197002, A196996, A197000.

Programs

Mathematica

c = Pi/6;
xo = x /.  FindRoot[x == Sin[x + c] Cos[x + c], {x, .8, 1.2}, WorkingPrecision -> 100]
RealDigits[xo] (* A197006 *)
m = 1/Sin[xo + c]
RealDigits[m] (* A197007 *)
yo = m*xo
d = Sqrt[xo^2 + yo^2]
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,
AspectRatio -> Automatic, AxesOrigin -> Automatic]