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A196620 Decimal expansion of the slope (negative) of the tangent line at the point of tangency of the curves y=cos(x) and y=(1/x)-c, where c is given by A196619.

%I A196620 #10 Aug 22 2018 05:06:58
%S A196620 8,7,6,3,4,6,2,0,1,1,1,8,3,7,4,1,9,1,1,2,3,4,9,4,1,1,3,9,2,2,8,3,0,2,
%T A196620 4,8,2,1,3,1,7,7,2,3,5,9,5,9,6,9,0,8,7,6,1,6,9,6,2,3,0,2,0,2,9,3,8,2,
%U A196620 0,9,1,7,8,1,6,7,8,2,2,6,2,7,5,1,0,3,9,1,6,7,7,6,2,9,9,4,5,2,1,3,1
%N A196620 Decimal expansion of the slope (negative) of the tangent line at the point of tangency of the curves y=cos(x) and y=(1/x)-c, where c is given by A196619.
%H A196620 G. C. Greubel, <a href="/A196620/b196620.txt">Table of n, a(n) for n = 0..10000</a>
%e A196620 x = -0.87634620111837419112349411392283024821317...
%t A196620 Plot[{1/x - .4544, Cos[x]}, {x, 0, 2 Pi}]
%t A196620 xt = x /. FindRoot[x^(-2) == Sin[x], {x, .5, .8}, WorkingPrecision -> 100]
%t A196620 RealDigits[xt]      (* A196617 *)
%t A196620 Cos[xt]
%t A196620 RealDigits[Cos[xt]] (* A196618 *)
%t A196620 c = N[1/xt - Cos[xt], 100]
%t A196620 RealDigits[c]       (* A196619 *)
%t A196620 slope = -Sin[xt]
%t A196620 RealDigits[slope]   (* A196620 *)
%o A196620 (PARI) a=1; c=0; x=solve(x=1, 1.5, a*x^2 + c - 1/sin(x)); -sin(x) \\ _G. C. Greubel_, Aug 22 2018
%Y A196620 Cf. A196619.
%K A196620 nonn,cons
%O A196620 0,1
%A A196620 _Clark Kimberling_, Oct 05 2011
%E A196620 Terms a(86) onward corrected by _G. C. Greubel_, Aug 22 2018