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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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