"Sinusoidal" in DSP terminology This is probably a bad question but I'll ask anyway because I'm often confused by it. Many textbooks explain how the movement of $z$ around the unit circle can be broken up into a sine wave along the horizontal axis axis and a cosine wave on the vertical axis. Both of these waves are termed sinusoidal.

So, if both of these are termed sinusoidal, then is the movement around the unit circle also termed "sinusoidal" or is it a combination of two sinusoids?
in my opinion, either of these two functions of time can be rightly labeled "sinusoidal":

$$ x(t) = A \sin(\omega t + \theta) $$

$$ y(t) = A e^{j(\omega t + \theta)} $$

where $A$, $\omega$ can be any non-zero real number (i wouldn't call DC a "sinusoid") and $\theta$ can be any real number.