Wording of a question

Wording of a question (vectors)

1. The problem statement, all variables and given/known data
I do not need help for a solution, I only need clarification on the question. I do not understand what the question is asking, here is a picture.

What does it mean when it says the rotation angle alpha? Are x' and y' two different vectors? Also what am I supposed to try to prove? Also what does point P have to do with anything?

 

So the question is saying to show that the coordinates (x,y) with respect to the normal Cartesian plane, are related to the different coordinates of that same point in the x',y' plane, with those equations. What is he exactly asking you to show? If he already gives you the solution. Is he asking your for the process in which you get those two expressions?