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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 Cartesian to Polar

The point \((5, 5\sqrt{3})\) in Cartesian coordinates can be expressed as \((r, \theta^{\circ})\) in polar coordinates, where \(r\) is a positive real number and \(0 \leq \theta \leq 180\). What is the value of \(r+ \theta\)?

The point \((-21\sqrt{3}, 21)\) in Cartesian coordinates can be expressed as \((r, \theta)\) in polar coordinates, where r is a positive real number and \(0^{\circ} \leq \theta \leq 180^{\circ}\). If \(\theta\) is measured in degrees, what is the value of \(r+ \theta\)?

If point \(P\) is given in Cartesian coordinates as \(P=(15, 15),\) what are the polar coordinates of \(P?\)

The point \((19, -19)\) in Cartesian coordinates can be expressed as \((r\sqrt{2}, \theta^{\circ})\) in polar coordinates, where \(r\) is a positive real number and \(0 \leq \theta \leq 360.\) What is the value of \(r+ \theta\)?

The point \((-19\sqrt{2}, 19\sqrt{2})\) in Cartesian coordinates can be expressed as \((r, \theta)\) in polar coordinates, where \(r\) is a positive real number and \(0^{\circ} \leq \theta \leq 180^{\circ}\). If \(\theta\) is measured in degrees, what is the value of \(r+\theta\)?

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