For the first part you will need to change variables in an equation.You will need to use this idea:

${\displaystyle \frac{\mathrm{df}}{\mathrm{dr}}=\frac{\mathrm{df}}{\mathrm{du}}\frac{\mathrm{du}}{\mathrm{dr}}}$

For the second part, you need to redefine your angle by shifting it by a certain amount.