Proving Rotation of Conic Using Polar Equations: Am I on the Right Track?

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The discussion revolves around proving the rotation of conics using polar equations, specifically by substituting Cartesian coordinates with polar coordinates. The user has successfully expressed x' and y' in terms of r and angles but is unsure if they are on the right track. They reference their textbook's matrix proof and seek clarification on the relationships between polar coordinates and Cartesian coordinates. Questions arise about the definitions of rsin(alpha) and rcos(alpha) in this context. The conversation highlights the challenges of transitioning from Cartesian to polar forms in geometric proofs.
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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
 

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Line up the corresponding equations.

What is rsin(alpha)? and rcos(alpha)?
 
robphy said:
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?
 

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