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.

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, 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, 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

Offset: 0

Author

Clark Kimberling, Oct 05 2011

Keywords

• nonn
• cons

Examples

			x = -0.87634620111837419112349411392283024821317...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A196619.

Programs

Mathematica

Plot[{1/x - .4544, Cos[x]}, {x, 0, 2 Pi}]
xt = x /. FindRoot[x^(-2) == Sin[x], {x, .5, .8}, WorkingPrecision -> 100]
RealDigits[xt]      (* A196617 *)
Cos[xt]
RealDigits[Cos[xt]] (* A196618 *)
c = N[1/xt - Cos[xt], 100]
RealDigits[c]       (* A196619 *)
slope = -Sin[xt]
RealDigits[slope]   (* 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

Extensions

Terms a(86) onward corrected by G. C. Greubel, Aug 22 2018