A197005 Decimal expansion of the slope of the line y=mx which meets the curve y=cos(x+Pi/3) orthogonally over the interval [0, 2*Pi] (as in A197004).

1, 0, 3, 7, 0, 5, 7, 0, 8, 3, 7, 3, 6, 5, 1, 5, 0, 0, 4, 6, 6, 1, 4, 7, 9, 5, 8, 3, 7, 5, 8, 4, 2, 7, 7, 6, 0, 5, 2, 2, 2, 3, 4, 3, 4, 3, 1, 3, 9, 2, 5, 1, 5, 3, 1, 6, 5, 5, 2, 9, 5, 2, 4, 2, 0, 6, 8, 4, 8, 7, 9, 8, 7, 2, 3, 9, 7, 5, 1, 8, 7, 8, 7, 4, 8, 1, 7, 2, 3, 2, 2, 4, 5, 5, 9, 3, 3, 2, 8, 0, 8, 9

Offset: 1

Author

Clark Kimberling, Oct 10 2011

Keywords

• nonn
• cons

Comments

See the Mathematica program for a graph.

xo=0.255465286103853596695882696613320272654788...

yo=0.264932084602776862434116494762571068650190...

m=1.0370570837365150046614795837584277605222343...

|OP|=0.3680373919265496189530095416155881110455...

Crossrefs

Cf. A197004, A197002, A196996, A197000.

Programs

Mathematica

c = Pi/3;
xo = x /.  FindRoot[x == Sin[x + c] Cos[x + c], {x, .8, 1.2}, WorkingPrecision -> 100]
RealDigits[xo] (* A197004 *)
m = 1/Sin[xo + c]
RealDigits[m]  (* A197005 *)
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]