Suppose you graph the function r(0) = 4cos (20) on the interval [0,2π] in polar coordinates. How many times do you think the graph will pass through the origin on interval? How many distinct "loops will the graph make? See if you can anticipate the answers to these questions either using algebra or graphing by hand. Then, use a graphing calculator or Desmos to verify your guess. Repeat everything from the previous problem, but this time with the function: r(0) = 4cos (30).
Suppose you graph the function r(0) = 4cos (20) on the interval [0,2π] in polar coordinates. How many times do you think the graph will pass through the origin on interval? How many distinct "loops will the graph make? See if you can anticipate the answers to these questions either using algebra or graphing by hand. Then, use a graphing calculator or Desmos to verify your guess. Repeat everything from the previous problem, but this time with the function: r(0) = 4cos (30).
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Repeat everything from the previous problem, but this time with the function:
![**Problem 8: Graphing Polar Functions**
Suppose you graph the function \( r(\theta) = 4\cos(2\theta) \) on the interval \([0, 2\pi]\) in polar coordinates. Consider the following questions:
- How many times do you think the graph will pass through the origin on this interval?
- How many distinct "loops" will the graph make?
Try to anticipate the answers to these questions using either algebra or by graphing by hand. Then, use a graphing calculator or Desmos to verify your guess.
**Problem 9: Exploring Variations**
Repeat everything from the previous problem, but this time with the function:
\[ r(\theta) = 4\cos(3\theta) \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3e869531-958e-4f8b-997d-b908634d80a9%2Fad6b2ccd-21de-4a6a-b52f-701fa0103b3a%2Fdskg3r9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem 8: Graphing Polar Functions**
Suppose you graph the function \( r(\theta) = 4\cos(2\theta) \) on the interval \([0, 2\pi]\) in polar coordinates. Consider the following questions:
- How many times do you think the graph will pass through the origin on this interval?
- How many distinct "loops" will the graph make?
Try to anticipate the answers to these questions using either algebra or by graphing by hand. Then, use a graphing calculator or Desmos to verify your guess.
**Problem 9: Exploring Variations**
Repeat everything from the previous problem, but this time with the function:
\[ r(\theta) = 4\cos(3\theta) \]
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