|
|
A196619
|
|
Decimal expansion of the number c for which the curve y=cos(x) is tangent to the curve y=(1/x)-c, and 0<x<2*Pi.
|
|
5
|
|
|
4, 5, 4, 4, 5, 1, 8, 6, 6, 3, 5, 4, 2, 2, 6, 5, 9, 9, 8, 1, 9, 6, 9, 1, 1, 4, 6, 3, 2, 9, 5, 2, 3, 4, 0, 2, 8, 3, 6, 3, 4, 6, 9, 6, 1, 1, 7, 9, 5, 6, 7, 2, 2, 1, 8, 1, 1, 7, 2, 6, 3, 4, 1, 4, 5, 1, 2, 5, 7, 1, 7, 1, 7, 6, 6, 8, 0, 0, 5, 9, 9, 3, 4, 9, 4, 8, 5, 0, 9, 9, 7, 9, 0, 1, 6, 0, 2, 7, 2
(list;
constant;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,1
|
|
LINKS
|
|
|
EXAMPLE
|
x = 0.454451866354226599819691146329523402836346961...
|
|
MATHEMATICA
|
Plot[{1/x - .4544, Cos[x]}, {x, 0, 2 Pi}]
xt = x /. FindRoot[x^(-2) == Sin[x], {x, .5, .8}, WorkingPrecision -> 100]
Cos[xt]
c = N[1/xt - Cos[xt], 100]
slope = -Sin[xt]
|
|
PROG
|
(PARI) a=1; c=0; x=solve(x=1, 1.5, a*x^2 + c - 1/sin(x)); 1/x - cos(x) \\ G. C. Greubel, Aug 22 2018
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|