Why doesn't the sampling theorem work in this case?
The formula given is

$$ F_s &gt; 2F_{\mathrm{max}}$$

not 

$$ F_s \ge 2F_{\mathrm{max}}$$

otherwise it is possible that you could be sampling exactly on the zero crossing points. In practice you would choose sometime a bit higher. For example, CD audio uses 44100 Hz to represent signals up to 20000 Hz.