Regarding pedantry, an interesting (or not) thing to know about sampling theory is that it supports both positive and negative frequencies through complex sinusoids.

In the complex plane (real from left to right, imaginary from bottom to top):

a positive-frequency complex sinusoid would rotate CCW in a circle, a negative one CW. Each positive and negative frequency from 0 up to Fs/2 Hz gets

*its own distinct point* on the circle ... except for +/- Fs/2.

Both +Fs/2 and -Fs/2 get the same point (at 180° or z = -1), which can be viewed as aliasing. So you have to pick and agree on

*either *using + or -Fs/2, but then you're fine.

Phase shift is simply rotation along that circle. So Fs/2 (180°, the leftmost point on the circle at z = -1 + 0i) with a phase shift of -90° would be rotated CW to 90° (topmost point on the circle) at z = 0 + 1i. Notice how the real part is then zero.

Real signals (like music) can be defined the same way except that they are a sum of two points mirrored over the real axis such that the imaginary parts cancel, leaving only the real part. So real signals rotate both in part CCW and CW and sum to points along the real number line.

This destroys the possibility to distinguish between positive and negative frequencies, or calculate magnitude or angle.

That means that reconstruction of a real sinusoid with a frequency of Fs/2 becomes limited to the case with 0° phase shift:

In the worst case (90° out of phase), the real part becomes zero so the sampling process would produce only zeroes and the reconstruction would result in silence.

In the best case (0° in phase), the real part matches the input signal.

In any intermediate case, the real part will be lower than the input's amplitude, cos(phase) to be precise, and the phase will be off by the input's phase shift.