Frequency range for set of all discrete-time sinusoids Consider discrete time sinusoids of the form $$x[n] = \cos(\omega n) \ ,$$ where $n$ is an integer. What frequency range of $\omega$ would constitute all the possible sinusoids? I'm thinking that $0\leq\omega&lt;\pi$ would suffice, but my teacher tells me it's $-\pi\leq\omega&lt;\pi$.
assuming $\omega$ is real, if the form of $x[n]$ is how you've defined it above, your thinking is correct.  doesn't matter if it's $+\omega$ or $-\omega$, the sinusoid behaves exactly the same.  if instead, the sinusoid had form

$$ x[n] = e^{j \omega n}  \ ,$$ 

then your teacher would be correct.