A196620 - OEIS

%I #10 Aug 22 2018 05:06:58

%S 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 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 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 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 G. C. Greubel, <a href="/A196620/b196620.txt">Table of n, a(n) for n = 0..10000</a>

%e x = -0.87634620111837419112349411392283024821317...

%t Plot[{1/x - .4544, Cos[x]}, {x, 0, 2 Pi}]

%t xt = x /. FindRoot[x^(-2) == Sin[x], {x, .5, .8}, WorkingPrecision -> 100]

%t RealDigits[xt]      (* A196617 *)

%t Cos[xt]

%t RealDigits[Cos[xt]] (* A196618 *)

%t c = N[1/xt - Cos[xt], 100]

%t RealDigits[c]       (* A196619 *)

%t slope = -Sin[xt]

%t RealDigits[slope]   (* A196620 *)

%o (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 Cf. A196619.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Oct 05 2011

%E Terms a(86) onward corrected by _G. C. Greubel_, Aug 22 2018