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