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...
Related questions
Question
![**Convert the rectangular equation to polar form.**
\[ xy = 14 \]
**Solution:**
In rectangular coordinates:
- \( x \) is the horizontal coordinate.
- \( y \) is the vertical coordinate.
In polar coordinates:
- \( r \) is the distance from the origin.
- \( \theta \) is the angle measured counterclockwise from the positive \( x \)-axis.
Using the relationships between rectangular and polar coordinates:
\[ x = r \cos(\theta) \]
\[ y = r \sin(\theta) \]
Substitute these into the given equation:
\[ (r \cos(\theta))(r \sin(\theta)) = 14 \]
This simplifies to:
\[ r^2 \cos(\theta) \sin(\theta) = 14 \]
Hence, the polar form of the given rectangular equation is:
\[ r^2 \cos(\theta) \sin(\theta) = 14 \]
**Graph/Diagram Description:**
There is no graph or diagram associated with this problem. There is a text box below the equation where the polar form solution would be entered.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc51a27f7-e004-47b6-8023-544dc66e83a5%2F16453e50-daee-4ed9-b797-fb2adacb0165%2Fzxf4lb9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Convert the rectangular equation to polar form.**
\[ xy = 14 \]
**Solution:**
In rectangular coordinates:
- \( x \) is the horizontal coordinate.
- \( y \) is the vertical coordinate.
In polar coordinates:
- \( r \) is the distance from the origin.
- \( \theta \) is the angle measured counterclockwise from the positive \( x \)-axis.
Using the relationships between rectangular and polar coordinates:
\[ x = r \cos(\theta) \]
\[ y = r \sin(\theta) \]
Substitute these into the given equation:
\[ (r \cos(\theta))(r \sin(\theta)) = 14 \]
This simplifies to:
\[ r^2 \cos(\theta) \sin(\theta) = 14 \]
Hence, the polar form of the given rectangular equation is:
\[ r^2 \cos(\theta) \sin(\theta) = 14 \]
**Graph/Diagram Description:**
There is no graph or diagram associated with this problem. There is a text box below the equation where the polar form solution would be entered.
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.Recommended textbooks for you
![Calculus: Early Transcendentals](https://www.bartleby.com/isbn_cover_images/9781285741550/9781285741550_smallCoverImage.gif)
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
![Thomas' Calculus (14th Edition)](https://www.bartleby.com/isbn_cover_images/9780134438986/9780134438986_smallCoverImage.gif)
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
![Calculus: Early Transcendentals (3rd Edition)](https://www.bartleby.com/isbn_cover_images/9780134763644/9780134763644_smallCoverImage.gif)
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
![Calculus: Early Transcendentals](https://www.bartleby.com/isbn_cover_images/9781285741550/9781285741550_smallCoverImage.gif)
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
![Thomas' Calculus (14th Edition)](https://www.bartleby.com/isbn_cover_images/9780134438986/9780134438986_smallCoverImage.gif)
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
![Calculus: Early Transcendentals (3rd Edition)](https://www.bartleby.com/isbn_cover_images/9780134763644/9780134763644_smallCoverImage.gif)
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
![Calculus: Early Transcendentals](https://www.bartleby.com/isbn_cover_images/9781319050740/9781319050740_smallCoverImage.gif)
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
![Precalculus](https://www.bartleby.com/isbn_cover_images/9780135189405/9780135189405_smallCoverImage.gif)
![Calculus: Early Transcendental Functions](https://www.bartleby.com/isbn_cover_images/9781337552516/9781337552516_smallCoverImage.gif)
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning