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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.

Converting Polar Coordinates

         

The point \( \left(12, \frac{3\pi}{4} \right)\) in polar coordinates can be expressed as \((a, b)\) in Cartesian coordinates, where \(a\) and \(b\) are real numbers. What is the value of \(-ab?\)

Suppose that \((a, \frac{\pi}{6})\) in polar coordinates represents the same point as \((b, 7)\) in Cartesian coordinates. What is the value of \(a^2+b^2\)?

\(P=(24, \frac{\pi}{3})\) in polar coordinates can be expressed as \(P=(a, b)\) in Cartesian coordinates. What is the value of \(a+b^2\)?

If point \(P\) is given in polar coordinates as \(P=\left(-10, \frac{3\pi}{4}\right),\) what are the Cartesian coordinates of \(P?\)

In polar coordinates, the graph of \(r = 46 \sin(\theta)\) is a circle. What is the radius of this circle?

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