A197009 - OEIS

%I #11 Apr 10 2021 02:04:34

%S 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,

%T 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,

%U 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

%N 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).

%C See the Mathematica program for a graph.

%C xo=0.277097976418521518914833086895...

%C yo=0.289494183027862650094360757305...

%C m=1.0447358251025919644670467125044...

%C |OP|=0.4007370341535820008719293563...

%H G. C. Greubel, <a href="/A197009/b197009.txt">Table of n, a(n) for n = 1..10000</a>

%e 1.044735825102591964467046712504404113048658932805059578874283182084650....

%t c = 1;

%t xo = x /. FindRoot[x == Sin[x + c] Cos[x + c], {x, .8, 1.2}, WorkingPrecision -> 100]

%t RealDigits[xo] (* A179378 *)

%t m = 1/Sin[xo + c]

%t RealDigits[m]  (* A197009 *)

%t yo = m*xo

%t d = Sqrt[xo^2 + yo^2]

%t Show[Plot[{Cos[x + c], yo - (1/m) (x - xo)}, {x, -Pi/4, Pi/2}],

%t ContourPlot[{y == m*x}, {x, 0, Pi}, {y, 0, 1}], PlotRange -> All,

%t AspectRatio -> Automatic, AxesOrigin -> Automatic]

%o (PARI) default(realprecision, 100); 1/sin(1 + solve(x=0, 2, x-sin(x+1)*cos(x+1))) \\ _G. C. Greubel_, Nov 16 2018

%Y Cf. A179378, A197002, A196996, A197000.

%K nonn,cons

%O 1,3

%A _Clark Kimberling_, Oct 10 2011