I need help with the following trigonometric development:
$ x = r(\theta)\cos\theta$
$ y = r(\theta)\sin\theta$
this gives:
$ x' = r'(\theta)\cos\theta - r(\theta)\sin\theta$
$ y' = r'(\theta)\sin\theta + r(\theta)\cos\theta$
My problem is that I cannot understand this development:
$(x')^2 + (y')^2 = r(\theta)^2 + r'(\theta)^2$
Can someone please explain to me how the last development is made and how you do / see that it is valid.
I am also a bit puzzled about why $x'$ and $y'$ is not written $x'(\theta)$ & $y'(\theta)$.
Thank you!