1. Consider the curve \(r = \cos(2\theta)\) in polar coordinates.
   1. What’s an equation (expressed in rectangular coordinates) of the line tangent to the curve at the point where \(\theta = \frac{\pi}{6}?\)
   2. What’s the area contained within a single “petal” of this curve?
   3. What’s the arclength of a single “petal”?
2. Consider the curve \(r = 3+ 3\sin(\theta)\) in polar coordinates.
   1. What’s an equation (expressed in rectangular coordinates) of the line tangent to the curve at the point where \(\theta = \frac{\pi}{4}?\)
   2. What’s the area of the region bound by this curve?
   3. What is the length of this curve?