What causes alternating patterns in the graph of tan(x)/cos(x)?

[AdrianHudson]

I just recently discovered for myself this weird graph, can anyone explain to me what is exactly happening here. I realize there are a couple asymptotes but I am confused on when when y<0 the "legs" of the graph converge on another asymptote it looks like the tan(x) is just repeated but flipped so it goes:
Normal tan(x) look then the second one will be tan(x) with a flip on the y-axis then it goes back to the normal tan(x) graph. Weird. Care to explain what's happens?

P.S sorry about if this is in the wrong section :)

 

[AdrianHudson]

Sorry about little typos I'm on my phone.

 

[lurflurf]

Plot tan(x) and tan(x)/cos(x) on the same axis
http://www.wolframalpha.com/input/?i=plot+{tan(x)/cos(x),tan(x)}

What is happening is
when cos(x)>0 to tan(x)/cos(x) looks a lot like tan(x)
when cos(x)<0 to tan(x)/cos(x) looks a lot like -tan(x)
So those two are alternating.