I am trying to understand a simple calculation in polar coordinates - and I am getting totally discombobulated (the original source can be found: here).
Please have a look at the following picture:
My questions
(1) I don't understand how the length labeled $dr \over d \theta$ can possibly be the change of $r$ with respect to a change in $\theta$.
(2) It is then said that $tan \alpha = {r \over {dr \over d \theta}}$. But how can you calculate the tan-function if you don't even have a right angled triangle - and anyway, the formular would suggest that you calculate the tan of the angle that is not labeled in the pic (because $tan={opposite \over adjecent}$)
Sorry, if this is too elementary - but it really bothers me right now... Thank you!