What does spectrum of sin(t) looks like in real life?

Question

In real life, negative frequency doesn't exist.

But x(t) = sin(t) has 2 spikes at -1 and 1 in X(w), corresponding to f = +- 1/2pi.

So what does the spectrum of sin(t) looks like in real life? Does it only have 1 big spike at f = 1/2pi? If so, how can it be distinguished from cos(t)?

Thank you. Edit: by real life, I mean what is the output when you measure the signal with a frequency analyzer (that must exist, right?)

Answer 1

Imagine that there is a spinning disk with an object sitting on it. And you are looking at the object side on. You will see the object moving back and forth in a classic sine wave.

Now from just the displacement of the object can you tell if the disk is moving clockwise or counterclockwise?

The negative frequency value corresponds to the clockwise spinning disk. However since $sin(x) = -sin(-x)$ a clockwise spinning disk and a counter clockwise spinning disk with the object placed on the opposite side of the disk look identical.

So the Fourier transform reflects both of these solutions.