$\displaystyle \text{Use}\:\begin{Bmatrix}x'\:=\:xcos\theta+ysin \theta & [1] \\ y' \:=\:ycos\theta-xsin\theta & [2] \end{Bmatrix}$

$\displaystyle \text{To make}\:\begin{Bmatrix}x\:=\:x'cos\theta-y'sin \theta & [1] \\ y \:=\:y'cos\theta+x'sin\theta & [2] \end{Bmatrix}$

My book is asking me to find this before the chapter is over, it is quite puzzling and one of the toughest questions at the end of the lesson.