![Precalculus](https://www.bartleby.com/isbn_cover_images/9780321716835/9780321716835_largeCoverImage.gif)
To find: Identify the polar equation and graph it.
![Check Mark](/static/check-mark.png)
Answer to Problem 56AYU
Solution
The graph of is an equation of Spiral.
Given:
It is asked to identify and graph the polar equation .
Explanation of Solution
Check for symmetry test:
Polar axis:
Replace by . The result is .
The test fails, so the graph may or may not symmetric with respect to the polar axis.
The line
: Replace by . The result is
The test fails, so the graph may or may not symmetric with respect to the line
The Pole:
Replace by . Then the result is , so , This test fails. Replace by . The result is
This test also fails, so the graph may or may not be symmetric with respect to the pole.
Furthermore, there is no number for which , so the graph does not pass through the pole. Observe that is positive for all , increases as increases, as .
Let’s find the values from to to get single line spiral.
To sketch:
.
Chapter 9 Solutions
Precalculus
Additional Math Textbook Solutions
University Calculus: Early Transcendentals (4th Edition)
Calculus: Early Transcendentals (3rd Edition)
Calculus, Single Variable: Early Transcendentals (3rd Edition)
Calculus: Early Transcendentals (2nd Edition)
Glencoe Math Accelerated, Student Edition
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning
![Text book image](https://www.bartleby.com/isbn_cover_images/9781285741550/9781285741550_smallCoverImage.gif)
![Text book image](https://www.bartleby.com/isbn_cover_images/9780134438986/9780134438986_smallCoverImage.gif)
![Text book image](https://www.bartleby.com/isbn_cover_images/9780134763644/9780134763644_smallCoverImage.gif)
![Text book image](https://www.bartleby.com/isbn_cover_images/9781319050740/9781319050740_smallCoverImage.gif)
![Text book image](https://www.bartleby.com/isbn_cover_images/9780135189405/9780135189405_smallCoverImage.gif)
![Text book image](https://www.bartleby.com/isbn_cover_images/9781337552516/9781337552516_smallCoverImage.gif)