This place has been great in helping me to understand my online image and signals class!
I've moved on to another question and wanted to see if I'm correctly grasping the subject. The next question is as follows:
If we sample a pure sine signal at "sam" samples per second, and there are 8 samples per cycle of the signal, and we have not undersampled the signal, what is the signal's frequency in cycles per second?
So using the Nyquist-Shannon theorem I know I have a Nyquist rate of $8\frac{samples}{cycle}$ so I believe to calculate the signals frequency in cycles per second I need to do the following:
$8\frac{sam}{cycle} = 2\,f_{max}$
$8\frac{sam}{cycle} = 2\left(\frac{sam}{sec}\right)$
$4\frac{sam}{cycle} = \frac{sam}{sec}$
$\frac{sam}{sam}=\frac{1}{4}\frac{cycle}{sec}$