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Chapter 10: Problem 1

Fill in the blank(s). The origin of the polar coordinate system is called the _____.

Short Answer

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

Step by step solution

01

Identification of the origin

The origin of the polar coordinate system is the point where the polar coordinate lines intersect. This usually corresponds to the point (0,0) in a Cartesian coordinate system.
02

Naming of the origin

In a polar coordinate system, the origin is known as the pole.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Origin
In coordinate systems, the origin is a key concept that helps us locate points. It is where all measurements start.
In the Cartesian coordinate system, the origin is the point (0,0), where the x and y axes intersect.
The polar coordinate system, however, views the origin differently. Here, the origin is called the pole.
  • Origin in Cartesian vs. Polar: In Cartesian, it's (0,0); in Polar, it's the pole.
  • Starting Point: The origin is the reference point from which all other points are measured for their distance and position.
To put it simply, the origin acts as the starting line for plotting points in any coordinate system.
Pole
In the polar coordinate system, the concept of the pole is central. Much like the origin in the Cartesian system, the pole is the point where all radial lines meet.
This point is always considered as the starting point of any measurement in polar coordinates.
The pole functions similarly to how a compass needle always points north when determining direction.
  • Intersection Point: It's where all circles in the polar system center.
  • Reference in Measurement: Distances (or radii) are measured from the pole.
  • Role in Navigation: It serves as a fixed point, often aiding in navigation and plotting paths.
Coordinate Systems
Coordinate systems are frameworks for identifying the position of points in space. Most commonly, these systems include the Cartesian and polar systems.
Each system has its own way to define a point's location.
Understanding these systems can help in visualizing and solving complex geometry problems.
  • Different Systems: Cartesian uses x and y axes, while polar uses a radius and angle.
  • Applications: Cartesian for straight lines, while polar is excellent for circular paths.
  • Conversion: You can convert between systems; however, each is best suited for specific types of problems.
These systems help in different fields like engineering, navigation, and graphics design, making them incredibly important for different applications.

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Most popular questions from this chapter

Convert the rectangular equation to polar form. Assume \(a<0\) $$x^{2}+y^{2}-2 a x=0$$

What conic does the polar equation \(r=a \sin \theta+b \cos \theta\) represent?

Convert the polar equation to rectangular form. $$r=\frac{6}{2-3 \sin \theta}$$

Use a graphing utility to graph the rotated conic. $$r=\frac{9}{3-2 \cos (\theta+\pi / 2)}$$

Find a polar equation of the conic with its focus at the pole. $$\begin{array}{cc} \text{Conic} & \text{Vertex or Vertices} \\\ \text{Ellipse} &(20,0),(4, \pi)\end{array}$$
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