cp's OEIS Frontend

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).

%I A197009 #11 Apr 10 2021 02:04:34
%S A197009 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 A197009 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 A197009 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 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).
%C A197009 See the Mathematica program for a graph.
%C A197009 xo=0.277097976418521518914833086895...
%C A197009 yo=0.289494183027862650094360757305...
%C A197009 m=1.0447358251025919644670467125044...
%C A197009 |OP|=0.4007370341535820008719293563...
%H A197009 G. C. Greubel, <a href="/A197009/b197009.txt">Table of n, a(n) for n = 1..10000</a>
%e A197009 1.044735825102591964467046712504404113048658932805059578874283182084650....
%t A197009 c = 1;
%t A197009 xo = x /. FindRoot[x == Sin[x + c] Cos[x + c], {x, .8, 1.2}, WorkingPrecision -> 100]
%t A197009 RealDigits[xo] (* A179378 *)
%t A197009 m = 1/Sin[xo + c]
%t A197009 RealDigits[m]  (* A197009 *)
%t A197009 yo = m*xo
%t A197009 d = Sqrt[xo^2 + yo^2]
%t A197009 Show[Plot[{Cos[x + c], yo - (1/m) (x - xo)}, {x, -Pi/4, Pi/2}],
%t A197009 ContourPlot[{y == m*x}, {x, 0, Pi}, {y, 0, 1}], PlotRange -> All,
%t A197009 AspectRatio -> Automatic, AxesOrigin -> Automatic]
%o A197009 (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 A197009 Cf. A179378, A197002, A196996, A197000.
%K A197009 nonn,cons
%O A197009 1,3
%A A197009 _Clark Kimberling_, Oct 10 2011