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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.
4
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
0,1
LINKS
EXAMPLE
x = -0.87634620111837419112349411392283024821317...
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 *)
PROG
(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
CROSSREFS
Cf. A196619.
Sequence in context: A334424 A021537 A208934 * A200598 A021846 A201579
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Oct 05 2011
EXTENSIONS
Terms a(86) onward corrected by G. C. Greubel, Aug 22 2018
STATUS
approved