Calculus of Polar Coordinates

Hello!

I have a couple questions that are tricky, given a curve

$\displaystyle C: r=\sqrt{cos(2\theta)} $ for $\displaystyle -\pi/4 \leq \theta < \pi/4 $

1) show that the slope of the tangent to a curve C at theta is given by

$\displaystyle m=-cot(3\theta)$

-for this, I have started with the fact, x=rcos(theta) and y=rsin(theta), substituting the value of r to get dy/d(theta) and dx/d(theta), then their quotient would be dy/dx...? not sure if that is a solid approach..

2) Show that C has arc length that can be represented

$\displaystyle \int_{-\pi/4}^{\pi/4} \sqrt{sec(2\theta)}d\theta $

thanks!!