Proving rotation transformation formulas using polar equations

[ballahboy]

Ok. So i got that part where you replace x with x'cos(theta)+y'sin(theta) and y with -x'sin(theta)+y'cos(theta). My book shows us the proof for this using matrices. What my teacher wants us to do its prove this using polar equations or something like that.

I started out with the drawing attached(teacher told us to use it). From that i got x'=rcos(theta-alpha) and y'=rsin(theta-alpha). Using the difference identities, i got x'=rcos(theta)cos(alpha)+rsin(theta)sin(alpha) and y'=rsin(theta)cos(alpha)-rcos(theta)sin(alpha). I kinda got stuck after this.. Am i on the right track at all? or is it completely off

 

[robphy]

Line up the corresponding equations.

What is rsin(alpha)? and rcos(alpha)?

 

[ballahboy]

What is rsin(alpha)? and rcos(alpha)?

umm.. iono about that but I know that rsin(theta) is y and rcos(theta) is x.. would that be the same?