Region D in Polar Coord

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In summary, Region D in Polar Coord is the second quadrant in a polar coordinate system with a theta angle between 90 and 180 degrees. It is represented by points with positive radius and negative theta values. The coordinates of points in this region are (r, -θ). Real-life examples of Region D include the position of a boat or plane traveling northeast, storm movement, and satellite orbits. In mathematics and science, Region D is used for data representation and analysis, as well as in navigation, astronomy, and engineering applications.
  • #1
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How would you write the region D given by

[tex]
\[D: \left\{
\begin{array}{l l}
\frac{-d}{2} \leq y \leq \frac{d}{2} \\
-\infty < x < \infty \\ \end{array} \right. \]
[/tex]

in polar coordinates?
 
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  • #2
first think about how you write the equation of a straight line in polar coord...
 
  • #3
Or, more specifically, how to write x and y in polar coordinates. Replace x and y in the inequalities with those and solve the inequalities.
 

1. What is Region D in Polar Coord?

Region D in Polar Coord refers to the area in a polar coordinate system where the theta angle is between 90 and 180 degrees. This region is also known as the second quadrant.

2. How is Region D represented in a polar coordinate system?

In a polar coordinate system, Region D is represented by points with positive values for the radius and negative values for the theta angle.

3. What are the coordinates of points in Region D?

The coordinates of points in Region D are in the form (r, -θ), where r is the distance from the origin and θ is the angle in degrees or radians.

4. What are some real-life examples of Region D in Polar Coord?

Some real-life examples of Region D in Polar Coord include the position of a boat or plane traveling northeast, the direction and distance of a storm moving southeast, and the location of a satellite orbiting the Earth in a counterclockwise direction.

5. How is Region D used in mathematics and science?

Region D in Polar Coord is used in mathematics and science to represent and analyze data in a polar coordinate system. It is also used in applications such as navigation, astronomy, and engineering.

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