r = 1 – sin0, r=1

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Find the area of the region that lies inside the first curve and outside the second curve.

### Problem 24: Polar Equations

- **Equation 1**: \( r = 1 - \sin \theta \)
- **Equation 2**: \( r = 1 \)

#### Explanation:

The problem involves two polar equations. The first equation, \( r = 1 - \sin \theta \), represents a Limaçon. This type of curve is characterized by its distinct inner loop, dimple, or a cardioid shape, depending on specific parameters. In this case, the equation does not form a complete cardioid because the coefficient of \(\sin \theta\) is not equal to the constant term, 1.

The second equation, \( r = 1 \), describes a circle centered at the pole with a radius of 1. This is a basic polar graph where every point on the circle is equidistant from the center (the pole) by a distance of 1.

Visualizing these equations together on a polar coordinate system will help in understanding their relationship and intersection points. The graph of these equations can provide insights into their geometric properties and intersections.
Transcribed Image Text:### Problem 24: Polar Equations - **Equation 1**: \( r = 1 - \sin \theta \) - **Equation 2**: \( r = 1 \) #### Explanation: The problem involves two polar equations. The first equation, \( r = 1 - \sin \theta \), represents a Limaçon. This type of curve is characterized by its distinct inner loop, dimple, or a cardioid shape, depending on specific parameters. In this case, the equation does not form a complete cardioid because the coefficient of \(\sin \theta\) is not equal to the constant term, 1. The second equation, \( r = 1 \), describes a circle centered at the pole with a radius of 1. This is a basic polar graph where every point on the circle is equidistant from the center (the pole) by a distance of 1. Visualizing these equations together on a polar coordinate system will help in understanding their relationship and intersection points. The graph of these equations can provide insights into their geometric properties and intersections.
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