![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 51AYU
Solution
The graph of is an equation of rose with three petals.
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 satisfied. So the graph is 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.
Let’s identify points on the graph by assigning values to the angle and calculating the corresponding values of .
As the polar equation is symmetric about the line , it is enough to find the values from to .
To sketch:
.
Chapter 9 Solutions
Precalculus
Additional Math Textbook Solutions
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (4th Edition)
Precalculus Enhanced with Graphing Utilities (7th Edition)
University Calculus: Early Transcendentals (3rd Edition)
Thomas' Calculus: Early Transcendentals (14th 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)