Why do we take $x=\cos t$, $y=\sin t$ for a parametric circle when we can take the opposite? Both $x = \cos t$, $y = \sin t$ and $x = \sin t$, $y = \cos t$ describe a circle
So why is the first parameterization so commonly used in mathematics, and not the second?

Because $e^{it} = \cos t+i\sin t$ (but not only because of that).
