sampling a sinusoidal signal at the Nyquist rate
Noha, when the classical sampling theorem (Nyquist-Shannon) for baseband signals
is applied to an ideal sinusoidal of infinite extend of frequency $f_m$ Hertz
$$x(t) = \cos(2 \pi f_m t)$$ it's found that the signal must be sampled at a sampling frequency greater than $2 f_m$; i.e. 
$$f_s &gt; 2 f_m$$

Note that even though the selection of $f_s = 2 f_m$ would sufficiently work for most of the typical engineering signals, it will not work for an ideal sinusoidal signal. The reason is that the ideal sinusoidal has an exact impulse at the $f_s / 2$ frequency whereas most typical signals will not.

The practical solution is to use a sampling frequency slightly greater than the theoretical value given by the sampling theorem unless you are sure that there wont be any components at $f_s/2$.