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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.

Polar Coordinates - 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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