We've been using one type of coordinate system to do everything, namely measuring everything by using x,y,z components. Is this the only option? What if instead we kept track of where the rover is by recording r and theta. What would things look like?
- Draw the path of an object given by a polar curve. Describe the path using xy coordinates
- Reverse the above, so give rtheta from xy.
Are there other ways to describe things? Yes - infinitely many ways.
- Give another change of coordinates (maybe a rotation and expansion). Have them compute the differentials.
This is a great time to introduce matrices. Maybe even area through determinants. Maybe... We'll see. Might be too soon.