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A196775 Decimal expansion of the slope (negative) at the point of tangency of the curves y=c+1/x and y=sin(x), where c is given by A196774.

%I A196775 #9 Mar 06 2021 01:58:22
%S A196775 2,8,8,1,0,6,5,7,2,8,3,1,2,9,8,9,6,7,2,7,3,9,8,9,5,9,9,4,5,0,8,3,9,2,
%T A196775 5,3,4,5,5,0,0,3,4,9,2,3,1,6,1,2,3,0,3,1,5,7,6,3,1,8,7,8,6,9,3,8,2,3,
%U A196775 1,4,4,3,9,3,5,1,0,4,3,4,2,5,5,7,7,1,0,3,5,1,5,6,7,7,7,5,6,8,4,9
%N A196775 Decimal expansion of the slope (negative) at the point of tangency of the curves y=c+1/x and y=sin(x), where c is given by A196774.
%e A196775 x=-0.28810657283129896727398959945083925345500...
%t A196775 Plot[{1/x + .42, Sin[x]}, {x, 0, 2 Pi}]
%t A196775 t = x /. FindRoot[-1 == (x^2) Cos[x], {x, 1.5, 2.5}, WorkingPrecision -> 100]
%t A196775 RealDigits[t]    (* A196773 *)
%t A196775 c = N[-1/t + Sin[t], 100]
%t A196775 RealDigits[c]    (* A196774 *)
%t A196775 slope = N[-1/t^2, 100]
%t A196775 RealDigits[slope](* A196775 *)
%Y A196775 Cf. A196774.
%K A196775 nonn,cons
%O A196775 0,1
%A A196775 _Clark Kimberling_, Oct 06 2011