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A196611 Decimal expansion of the slope (negative) of the tangent line at the point of tangency of the curves y=c*cos(x) and y=1/x, where c is given by A196610.

%I A196611 #8 Sep 03 2022 22:47:10
%S A196611 1,3,5,1,0,3,3,8,8,6,8,7,8,3,7,8,6,2,4,0,0,9,1,9,2,4,7,3,5,2,8,4,3,0,
%T A196611 2,1,7,4,8,3,4,3,7,8,0,5,9,6,3,4,7,8,1,5,9,2,3,0,1,4,5,2,3,3,6,5,4,5,
%U A196611 9,5,8,9,8,3,5,7,6,8,7,7,2,4,9,2,4,5,3,5,7,8,7,6,5,3,0,2,9,4,9,4
%N A196611 Decimal expansion of the slope (negative) of the tangent line at the point of tangency of the curves y=c*cos(x) and y=1/x, where c is given by A196610.
%C A196611 For x>0, there is exactly one number c for which the graphs of y=c*cos(x) and y=1/x, where 0<x<2*Pi, have the same tangent line.
%e A196611 slope = -1.3510338868783786240091924735284302174...
%t A196611 Plot[{1/x, (1.78222) Cos[x]}, {x, .7, 1}]
%t A196611 xt = x /. FindRoot[x == Cot[x], {x, .8, 1}, WorkingPrecision -> 100]
%t A196611 c = N[Csc[xt]/xt^2, 100]
%t A196611 RealDigits[c]  (* A196610 *)
%t A196611 slope = -c*Sin[xt]
%t A196611 RealDigits[slope]  (* A196611 *)
%Y A196611 Cf. A196610, A196603.
%K A196611 nonn,cons
%O A196611 1,2
%A A196611 _Clark Kimberling_, Oct 04 2011