Graphing Polar Curves: Inner Loop with a Twist | Homework Help

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SUMMARY

The discussion revolves around graphing polar curves, specifically focusing on an inner loop graph represented by the equation r = 1 + 2sin(θ). The user initially struggles to derive the correct equation but ultimately finds the solution to be r = 2 + 5cos(θ). This indicates a transformation in the polar graph that alters the orientation of the inner loop. The key takeaway is understanding how the coefficients in polar equations affect the graph's shape and position.

PREREQUISITES
  • Understanding of polar coordinates and graphs
  • Familiarity with the polar equation format r = a + bsin(θ) or r = a + bcos(θ)
  • Basic knowledge of trigonometric functions and their properties
  • Ability to interpret graphical representations of mathematical equations
NEXT STEPS
  • Study the effects of varying coefficients in polar equations
  • Learn about graphing polar curves using software tools like Desmos or GeoGebra
  • Explore the concept of inner loops in polar graphs and their mathematical implications
  • Investigate transformations of polar equations and their graphical outcomes
USEFUL FOR

This discussion is beneficial for students studying polar coordinates, mathematics educators seeking teaching resources, and anyone interested in graphing polar equations effectively.

d.tran103
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Homework Statement


Hi, my teacher gave me this homework assignment and I'm having trouble graphing this one graph. I don't understand her notes that well and am having trouble getting the equation for this graph. See attached for the graph. The graph is a inner loop that is turned.


Homework Equations


The only notes my teacher gave me for this problem are: "A < B = inner loop, r = 1 + 2sin(theta).


The Attempt at a Solution


I think the equation is in the form, r = a + bsin(theta). But this gives me a graph with the inner loop coming from the bottom. My inner loop comes from the left. I've tried a couple of things to but can't figure out the pattern. Does anybody know a good website for learning these? I'm taking this class online and my teacher never responds to me. I was only given the above for notes. Thanks!
 

Attachments

  • Inner Loop.jpg
    Inner Loop.jpg
    22.9 KB · Views: 453
Physics news on Phys.org
Nevermind, I got it! r = 2+5cos(theta)
 

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