Precalculus with Limits: A Graphing Approach, Sixth Edition
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Precalculus with Limits: A Graphing Approach, Sixth Edition View details
5. Polar Coordinates
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Exercise 1 Page 681

We are asked to complete the following sentence.

The origin of the polar coordinate system is called the .

Let's start by recalling how we can construct the polar coordinate system in a plane. To do this, we need to fix a point O that will represent the origin of the polar coordinate system. Then, we can construct an initial ray from point O called the polar axis. That ray would look like the following diagram.
Polar coordinate system

Then, each point P in the plane can be assigned polar coordinates (r, θ), where r is the directed distance from O to P, and θ is the directed angle, counterclockwise from the polar axis to segment OP.

Polar coordinate system

Recall that the origin of the polar coordinate system is also called the pole. With this in mind, let's complete the sentence.

The origin of the polar coordinate system is called the pole.