Converting to Polar Coordinates
Convert the point from rectangular coordinates into polar coordinates with $r \geq 0$ and $0 \leq \theta<2 \pi$.
\[
(7,-7)
\]
Converting to Rectangular Coordinates
The polar coordinates of a point are $(-5, \pi)$. Find the rectangular coordinates of this point.
The rectangular coordinates are
(Simplify your answer. Type an ordered pair. Type an exact answer for each coordinate, using radicals as needed. Use integers or fractions for any numbers in the expression.)
Identifying and Graphing Circles
A circle is represented by the polar equation \(r = 3\cos(\theta)\). What is the center and the radius of this circle?
Identifying and Graphing Limacons
Identify and graph the limaçon described by the polar equation \( r = 1 + 2\cos{\theta} \).
Identifying and Graphing Roses
Identify the type of rose and graph it for the following polar equation: \( r = 3 \cos(2\theta) \)
Identifying and Graphing Cardioids
Given the polar equation \( r = 1 - 2\cos(\theta) \), identify the type of conic section and sketch the graph.