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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 Coordinates 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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