A197004 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/3) orthogonally.

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

Offset: 0

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. 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]