cp's OEIS Frontend

A197001 Decimal expansion of the slope of the line y=mx which meets the curve y=1+cos(x) orthogonally over the interval [0, 2*Pi] (as in A197000).

%I A197001 #10 Apr 10 2021 02:05:00
%S A197001 1,0,5,4,1,7,8,4,4,2,6,5,6,8,4,2,1,7,5,1,5,7,4,7,7,3,4,3,0,5,6,7,3,4,
%T A197001 8,3,7,4,6,1,4,2,1,0,4,5,8,9,1,6,0,6,6,4,5,3,6,7,7,2,1,8,5,0,7,8,2,3,
%U A197001 8,0,7,2,5,6,7,6,3,2,7,7,7,9,0,9,4,3,3,8,4,5,0,3,2,0,5,7,5,4,6,9,3
%N A197001 Decimal expansion of the slope of the line y=mx which meets the curve y=1+cos(x) orthogonally over the interval [0, 2*Pi] (as in A197000).
%C A197001 See the Mathematica program for a graph.
%C A197001 xo=1.2488014367215508560475125020128381535587614...
%C A197001 yo=1.3164595537507515212878992732671186100622603...
%C A197001 m=1.05417844265684217515747734305673483746142104...
%C A197001 |OP|=1.81454423617045980814297669595599066552030...
%t A197001 c = 1;
%t A197001 xo = x /.
%t A197001   FindRoot[x == Sin[x] (c + Cos[x]), {x, 1, 1.3}, WorkingPrecision -> 100]
%t A197001 RealDigits[xo] (* A197000 *)
%t A197001 m = 1/Sin[xo]
%t A197001 RealDigits[m]  (* A197001 *)
%t A197001 yo = m*xo
%t A197001 d = Sqrt[xo^2 + yo^2]
%t A197001 Show[Plot[{c + Cos[c*x], yo - (1/m) (x - xo)}, {x, 0, Pi}],  ContourPlot[{y == m*x}, {x, 0, Pi}, {y, 0, 2}], PlotRange -> All, AspectRatio -> Automatic, AxesOrigin -> Automatic]
%Y A197001 Cf. A196700, A196996, A197002.
%K A197001 nonn,cons
%O A197001 1,3
%A A197001 _Clark Kimberling_, Oct 09 2011