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Polar Coordinates

Polar coordinates are a way to describe where a point is on a plane. Instead of using x and y, you use the angle theta and radius r, to describe the angle and distance of the point from the origin.

Problem Solving


What is the polar equation of the above graph?

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 \(r=\frac{1}{2}\)?


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