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tch the polar equation with the graphs labeled I-VI. Use the table to help you. r = sin(40) OX III Need Help? Read It +++ 3 II e IV E VI +

tch the polar equation with the graphs labeled I-VI. Use the table to help you. r = sin(40) OX III Need Help? Read It +++ 3 II e IV E VI +

Trigonometry (11th Edition)
Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE: 1. Give the measures of the complement and the supplement of an angle measuring 35°.
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Question
**Polar Equations and Graphs** The image presents a task to match the polar equation \( r = \sin(4\theta) \) with one of the graphs labeled I-VI. Below are detailed descriptions of each graph: 1. **Graph I**: This graph shows a four-petaled flower, known as a "rose," centered at the origin. The petals are evenly spaced and symmetrically arranged around the center. 2. **Graph II**: This graph features a three-petaled flower, centered at the origin, usually referred to as a "limacon" with inner loops. 3. **Graph III**: This graph is a circle centered at the origin with radius 3. 4. **Graph IV**: This graph shows a limacon with a loop, having one small inner loop and one larger outer loop. 5. **Graph V**: This graph displays an eight-petaled rose, symmetrically arranged, with petals distributed evenly around the origin. 6. **Graph VI**: This graph is a circle centered at the origin with radius 3, similar to Graph III but reshaped slightly. **Task Instructions**: Match the provided polar equation \( r = \sin(4\theta) \) with the correct rose plot among the graphs. Recognize that \( r = \sin(4\theta) \) typically produces a four-petaled rose, implying Graph I is the potential match. **Tools**: Use available resources or visualizations like the included **table** to assist in identifying the correct graph. The option to "Submit Answer" is available at the bottom, with additional help accessible via the "Read It" button for further guidance.
Transcribed Image Text:**Polar Equations and Graphs** The image presents a task to match the polar equation \( r = \sin(4\theta) \) with one of the graphs labeled I-VI. Below are detailed descriptions of each graph: 1. **Graph I**: This graph shows a four-petaled flower, known as a "rose," centered at the origin. The petals are evenly spaced and symmetrically arranged around the center. 2. **Graph II**: This graph features a three-petaled flower, centered at the origin, usually referred to as a "limacon" with inner loops. 3. **Graph III**: This graph is a circle centered at the origin with radius 3. 4. **Graph IV**: This graph shows a limacon with a loop, having one small inner loop and one larger outer loop. 5. **Graph V**: This graph displays an eight-petaled rose, symmetrically arranged, with petals distributed evenly around the origin. 6. **Graph VI**: This graph is a circle centered at the origin with radius 3, similar to Graph III but reshaped slightly. **Task Instructions**: Match the provided polar equation \( r = \sin(4\theta) \) with the correct rose plot among the graphs. Recognize that \( r = \sin(4\theta) \) typically produces a four-petaled rose, implying Graph I is the potential match. **Tools**: Use available resources or visualizations like the included **table** to assist in identifying the correct graph. The option to "Submit Answer" is available at the bottom, with additional help accessible via the "Read It" button for further guidance.
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