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Section 6.5: Graphs of Polar Equations

Section 6.5: Graphs of Polar Equations. April 29, 2014. Families of Polar Graphs. Lemniscates Limacons Spiral of Archimedes Rose Curves. Analyzing Graphs. Look for these aspects of each graph: Domain Range Continuity Symmetry Boundedness , Max r-value Asymptotes. Rose Curves.

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Section 6.5: Graphs of Polar Equations

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  1. Section 6.5: Graphs of Polar Equations April 29, 2014

  2. Families of Polar Graphs • Lemniscates • Limacons • Spiral of Archimedes • Rose Curves

  3. Analyzing Graphs Look for these aspects of each graph: • Domain • Range • Continuity • Symmetry • Boundedness, Max r-value • Asymptotes

  4. Rose Curves • The general form of the equation for a rose curve is … r = a cos nθor r = a sin nθ. • In small groups, answer these questions: • How does the graph change if it is a cosine vs. sine graph? Symmetry? • What does the a value effect? Range? • What does the n value effect? Can you create a rule to describe the graphs based on the n-values?

  5. Rose Curve Summary

  6. Limacons • The general form of the equation for a limacon is … r = a ± bcosθor r = a ± b sin θ. • In small groups, answer these questions: • How does the graph change if it is a cosine vs. sine graph? Symmetry? • What does the a value effect? • What does the b value effect? • Can you create a rule to describe the graphs based on the relationship between a and b values? Range?

  7. Limacon Summary

  8. Lemniscates • The general form of the equation for a rose curve is … or . • In small groups, answer these questions: • How does the graph change if it is a cosine vs. sine graph? Symmetry? • What does the a value effect? Range?

  9. Spiral of Archimedes • The general form of the equation for a spiral is … r = nθ. • In small groups, answer these questions: • What does the a value effect? Symmetry? Direction of spiral?

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