cos (tan x)
For those curious what that crazy graph we were asked to draw earlier was actually supposed to look like, I draw it in Autograph.
Using my mathz skillz, I'm reckoning that those big blocks of black are the cos curve doing it's usual waving up and down between 1 and -1, it's just the ups and downs are getting closer and closer together as x tends to pi/2 (or multiple of pi/2). At x=pi/2, I think it's undefined. This is different to what y = tan x does at pi/2, which is tend to infinity. This means we're attempting cos of infinity. Picturing following the y = cos x graph along for larger and larger x values, it just does it's unchanging waving up and down. It doesn't tend to a specific value like tan does near pi/2. Therefore undefined. I'm assuming this means our graphs don't get the dotted lines that y = tan x does at it's asymptotes since it doesn't contain asymptotes.
Incidentally, I got curious as to what tan(cos x) looked like. A wierd kinda right angled thing (almost, the lines are slightly kinked). Here it is: tancos_x.agg