Compass Maths

So I sat down yesterday and tried to figure out how to use our single-axis compass give us the information we want.  Assuming that the (scaled) output ranges from +1 (we're aligned due North) to -1 (we're aligned due South), I discovered that it will require two single-axis compasses to give us the information we need.  Included below are the diagrams of how this works, including two ways of mapping inputs to outputs.  Pretty fantastic.