tabvar(sin(x)) question...

[webmasterpdx]

I think the arrows mean "increasing" and "decreasing".

I also did a simplify(|cot(pi*x)|^(1/16) - 10) and I got this as result:

_x->(table(_x+1 = (|cos(pi*x)|/|sin(pi*x)|)^(1/16) -10))

Please explain what this means?
Thx
-Donald