A197010 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+1/2) orthogonally.

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

Offset

0,1

Comments

See the Mathematica program for a graph.

xo=0.4672816053760121337816307268...

yo=0.5675398046001583628839615011...

m=1.21455627200105698029988016754...

|OP|=0.73515544514637791501789646...

Links

Table of n, a(n) for n=0..99.

Mathematica

c = 1/2;
xo = x /. FindRoot[x == Sin[x + c] Cos[x + c], {x, .8, 1.2}, WorkingPrecision -> 100]
RealDigits[xo] (* A197010 *)
m = 1/Sin[xo + c]
RealDigits[m]  (* A197011 *)
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]

Crossrefs

Cf. A179378, A197011, A197002, A196996, A197000.

Sequence in context: A200410 A136323 A135798 * A021218 A298974 A344983

Adjacent sequences: A197007 A197008 A197009 * A197011 A197012 A197013

Keyword

nonn,cons

Author

Clark Kimberling, Oct 10 2011

Status

approved