Plot the point given in polar coordinates. (3/2, 4.71) KIN

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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**Title: Plotting Points in Polar Coordinates**

**Description:**

This educational content focuses on plotting a point in polar coordinates and exploring multiple representations of that point.

**Point Given in Polar Coordinates:**
- \( (3\sqrt{2}, 4.71) \)

**Diagrams:**

Four polar coordinate graphs are displayed. Each graph features concentric circles centered at the origin, with angular divisions marked at \( \frac{\pi}{2} \), \( \pi \), \( \frac{3\pi}{2} \), and \( 2\pi \) (and equivalent angular measures in radians).

1. **Top-Left Graph:**
   - Displays a radius extending outward at an angle of \( 3\pi/2 \).

2. **Top-Right Graph:**
   - Displays a radius extending outward near the angle \( 4.71 \) radians (approximately \( 3\pi/2 \)).

3. **Bottom-Left Graph:**
   - Displays a radius extending outward at an obtuse angle, indicating a negative radial component.

4. **Bottom-Right Graph:**
   - Displays a radius extending outward at the angle \( \pi/2 \).

**Task:**

The task requires finding three additional polar representations of the given point, using the condition \(-2\pi < \theta < 2\pi\). Answers should be given in order of smallest to largest first by \( r \)-value, then by \(\theta\)-value. Answers should be rounded to two decimal places.

**Input Boxes:**

- \( (r, \theta) = \)
- \( (r, \theta) = \)
- \( (r, \theta) = \)

**Help Options:**

- **Read It**: Provides textual guidance.
- **Watch It**: Offers a visual explanation.

This content is designed to deepen understanding of polar coordinate systems, emphasizing both analytical and graphical comprehension.
Transcribed Image Text:**Title: Plotting Points in Polar Coordinates** **Description:** This educational content focuses on plotting a point in polar coordinates and exploring multiple representations of that point. **Point Given in Polar Coordinates:** - \( (3\sqrt{2}, 4.71) \) **Diagrams:** Four polar coordinate graphs are displayed. Each graph features concentric circles centered at the origin, with angular divisions marked at \( \frac{\pi}{2} \), \( \pi \), \( \frac{3\pi}{2} \), and \( 2\pi \) (and equivalent angular measures in radians). 1. **Top-Left Graph:** - Displays a radius extending outward at an angle of \( 3\pi/2 \). 2. **Top-Right Graph:** - Displays a radius extending outward near the angle \( 4.71 \) radians (approximately \( 3\pi/2 \)). 3. **Bottom-Left Graph:** - Displays a radius extending outward at an obtuse angle, indicating a negative radial component. 4. **Bottom-Right Graph:** - Displays a radius extending outward at the angle \( \pi/2 \). **Task:** The task requires finding three additional polar representations of the given point, using the condition \(-2\pi < \theta < 2\pi\). Answers should be given in order of smallest to largest first by \( r \)-value, then by \(\theta\)-value. Answers should be rounded to two decimal places. **Input Boxes:** - \( (r, \theta) = \) - \( (r, \theta) = \) - \( (r, \theta) = \) **Help Options:** - **Read It**: Provides textual guidance. - **Watch It**: Offers a visual explanation. This content is designed to deepen understanding of polar coordinate systems, emphasizing both analytical and graphical comprehension.
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