Algebra
Polar Coordinates
Consider the graphs of two polar functions \[r=6\sin \theta, r=1+\sin \theta.\] How many intersection points do they have?
What is the number of regions bounded by the polar curve \(r=\cos 2\theta\)?
If the two polar equations \[r=\frac{1}{\cos \theta -\sin \theta}, r^2=181\] are converted to Cartesian coordinates, what is the sum of the \(x\)-coordinates of all intersection points of the two curves?
How many times do the following curves in polar coordinates intersect \(r=\cos 4\theta\) and \(r=\frac{1}{2}\)?