Parametric Curves-Luke

The lab I have been looking at is on Parametric Curves. These are where you have two variables and a function that graphs them. But instead of using one function in terms of x and/or y:

$y=f(x)$ or $z=f(x,y)$,

parametric curves give the values for x and y as a function of t. So:

$x=x(t)$ and $y=y(t)$

This way of representing curves can be very useful with circles and polar coordinates. The questions that they ask deal mostly with parameters of $sin(at)$ and $cos(bt)$. The first few questions start exploring functions and seeing what they do with different values, how they intersect, etc. And then forming conjectures based on the data.