Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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### Problem Overview

**Objective:**
- a. Determine all intersection points of the given polar curves.
- b. Calculate the area enclosed by both curves.

**Given Curves:** 
- \( r = 23 + 23 \sin \theta \)
- \( r = 23 + 23 \cos \theta \)

### Part a: Finding Intersection Points

**Instructions:**
Identify all intersection points. Use \( 0 \) for the \( \theta \) coordinate at the pole if it is an intersection point.

**Input Format:**
- Type an ordered pair for \( \theta \) in radians.
- Use a comma to separate answers as needed.
- Provide exact answers using \(\pi\) as needed.

### Part b: Calculating Enclosed Area

Determine the area of the entire region that lies within both curves.

### Notes

- Ensure your solutions consider the symmetries and periodic nature of sine and cosine in polar coordinates.
- This problem involves matching radii and considering the angles where these functions equal each other.
- Remember that polar curves can intersect at multiple points, including diametrically opposite angles for \(\theta\).
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Transcribed Image Text:### Problem Overview **Objective:** - a. Determine all intersection points of the given polar curves. - b. Calculate the area enclosed by both curves. **Given Curves:** - \( r = 23 + 23 \sin \theta \) - \( r = 23 + 23 \cos \theta \) ### Part a: Finding Intersection Points **Instructions:** Identify all intersection points. Use \( 0 \) for the \( \theta \) coordinate at the pole if it is an intersection point. **Input Format:** - Type an ordered pair for \( \theta \) in radians. - Use a comma to separate answers as needed. - Provide exact answers using \(\pi\) as needed. ### Part b: Calculating Enclosed Area Determine the area of the entire region that lies within both curves. ### Notes - Ensure your solutions consider the symmetries and periodic nature of sine and cosine in polar coordinates. - This problem involves matching radii and considering the angles where these functions equal each other. - Remember that polar curves can intersect at multiple points, including diametrically opposite angles for \(\theta\).
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