cp's OEIS Frontend

A196997 Decimal expansion of m, where y=m*x is the line through (0,0) which meets the curve y=cos(3*x) orthogonally at a point (x,y) satisfying 0 < x < 2*Pi.

%I A196997 #9 Apr 10 2021 02:02:21
%S A196997 3,5,3,1,4,0,0,6,5,6,5,9,1,2,0,9,6,7,5,5,6,6,6,1,1,1,4,1,2,7,8,5,0,3,
%T A196997 1,9,5,4,3,7,5,6,8,5,5,0,1,6,0,6,6,8,4,3,1,8,7,7,3,8,6,5,9,0,5,2,8,4,
%U A196997 7,1,6,5,0,1,6,9,6,6,2,4,3,6,0,2,0,2,7,0,6,6,2,2,6,8,7,7,1,8,7
%N A196997 Decimal expansion of m, where y=m*x is the line through (0,0) which meets the curve y=cos(3*x) orthogonally at a point (x,y) satisfying 0 < x < 2*Pi.
%C A196997 See the Mathematica program for a graph.
%C A196997 xo=0.9350272884749678361451944275323...
%C A196997 yo=0.3301955980451199836007253971727...
%C A196997 m=0.35314006565912096755666111412785...
%C A196997 |OP|=0.99161744799152518925689622748...
%t A196997 c = 3;
%t A196997 xo = x /. FindRoot[0 == x + c*Sin[c*x] Cos[c*x], {x, .8, 1.2}, WorkingPrecision -> 100]
%t A196997 RealDigits[xo] (* A196996 *)
%t A196997 m = Sin[c*xo]/xo
%t A196997 RealDigits[m]  (* A196997 *)
%t A196997 yo = m*xo
%t A196997 d = Sqrt[xo^2 + yo^2]
%t A196997 Show[Plot[{Sin[c*x], yo - (1/m) (x - xo)}, {x, 0, Pi/c}], ContourPlot[{y == m*x}, {x, 0, 1.5}, {y, -.1, 1}], PlotRange -> All, AspectRatio -> Automatic]
%Y A196997 Cf. A196996, A197000, A197002.
%K A196997 nonn,cons
%O A196997 0,1
%A A196997 _Clark Kimberling_, Oct 09 2011