A197009 Decimal expansion of the slope of the line y=mx which meets the curve y=cos(x+1) orthogonally over the interval [0, 2*Pi] (as in A197006).

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

Offset: 1

Author

Clark Kimberling, Oct 10 2011

Keywords

• nonn
• cons

Comments

See the Mathematica program for a graph.

xo=0.277097976418521518914833086895...

yo=0.289494183027862650094360757305...

m=1.0447358251025919644670467125044...

|OP|=0.4007370341535820008719293563...

Examples

			1.044735825102591964467046712504404113048658932805059578874283182084650....
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A179378, A197002, A196996, A197000.

Programs

Mathematica

c = 1;
xo = x /. FindRoot[x == Sin[x + c] Cos[x + c], {x, .8, 1.2}, WorkingPrecision -> 100]
RealDigits[xo] (* A179378 *)
m = 1/Sin[xo + c]
RealDigits[m]  (* A197009 *)
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]

PARI

default(realprecision, 100); 1/sin(1 + solve(x=0, 2, x-sin(x+1)*cos(x+1))) \\ G. C. Greubel, Nov 16 2018