Confusion of finding asymtotes from trig function

I am having a hard time on comprehending where the asymptotes lie on a variety of trig questions.

y= sec(x/2) > [0,2pie]

-the help sheet clearly states that when plotting a sec graph, the asymptotes are located in the domain of [0,2pie] at pie/2 and 3pie/2, but the answer repels this and has the asymptotes at just pie. What am i doing wrong?

y= cot(3x) > [0,2pie]

-the help sheet clear states that the asymptotes are located in the domain of [0,2pie] at 0,pie and 2 pie, yet the answer locates the asymptotes at pie/3, 2pie/3, pie, 4pie/3, 5pie/3 and 2pie........why are there more than the normal amount? is it because there is a number in the brackets, making there more cycles therefor more asymptotes, i am unsure. It would be very helpful if someone could provide me with a bit of detail on this.