I'm reading a very general definition of parameter on this [site](http://mathinsight.org/definition/parameter).

I didn't understand why we call the variable $t$ of the curve $\alpha(t)=(\cos t,\sin t)$ a parameter.

For me $t$ in this case is a variable too according to the definition of the site I linked. If the definition of this site is right a parameter is either constant or change slower than the variable, which is not the case with this curve.