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Symmetry in Graphs of Polar Equations

Symmetry in Graphs of Polar Equations. On to Sec. 6.5a!!!. Recall our three types of symmetry…. 1. The x-axis (polar axis) as a line of symmetry. y. x. Recall our three types of symmetry…. 2. The y-axis (the line ) as a line of symmetry. y. x.

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Symmetry in Graphs of Polar Equations

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  1. Symmetry in Graphs of Polar Equations On to Sec. 6.5a!!!

  2. Recall our three types of symmetry… 1. The x-axis (polar axis) as a line of symmetry y x

  3. Recall our three types of symmetry… 2. The y-axis (the line ) as a line of symmetry y x

  4. Recall our three types of symmetry… 3. The origin (the pole) as a point of symmetry y x

  5. Symmetry Tests for Polar Graphs The graph of a polar equation has the indicated symmetry if either replacement produces an equivalent polar equation. To Test for Symmetry Replace By 1. about the x-axis 2. about the y-axis 3. about the origin

  6. Guided Practice Use symmetry tests to determine if the graph if symmetric about the x-axis, y-axis, or origin. Confirm your answers graphically. (check the graph first???) Symmetric about the y-axis

  7. Guided Practice Use symmetry tests to determine if the graph if symmetric about the x-axis, y-axis, or origin. Confirm your answers graphically. Symmetric about the x-axis

  8. Guided Practice Use symmetry tests to determine if the graph if symmetric about the x-axis, y-axis, or origin. Confirm your answers graphically. Symmetric about the y-axis

  9. Guided Practice Use symmetry tests to determine if the graph if symmetric about the x-axis, y-axis, or origin. Confirm your answers graphically. Symmetric about the y-axis

  10. Guided Practice Use symmetry tests to determine if the graph if symmetric about the x-axis, y-axis, or origin. Confirm your answers graphically. Symmetric about the x-axis

  11. Analyzing Graphs of Polar Equations

  12. But first… p.548: #1 3 0 –3 0 3 0 –3 0 Now, do you have the graph?

  13. We can “analyze” the graphs of polar equations in much the same way as we have for rectangular equations… As before, we check: Domain Range Symmetry Continuity Boundedness Asymptotes Maximum r-value (this is the new one…)

  14. Let’s focus on that last one for a bit… Find the maximum r-value of  Check algebraically and graphically… Maximum r-value = 4

  15. Let’s focus on that last one for a bit… Identify the points on the graph of for that give maximum r-values

  16. Guided Practice Analyze the graph of the given polar curve. The graph??? Domain: Range: Symmetry: About the x-axis, y-axis, and origin Continuity: Continuous Boundedness: Bounded Asymptotes: None Maximum r-value: 8

  17. Guided Practice Analyze the graph of the given polar curve. The graph??? Domain: Range: Symmetry: About the origin Continuity: Continuous Boundedness: Unbounded Asymptotes: None Maximum r-value: None

  18. One Last Definition The graphs of and where n is an integer greater than 1, are rose curves If n is odd there are n petals; if n is even there are 2n petals

  19. Analyze the graph: The graph??? How many petals??? Domain: Range: Symmetry: About the x-axis, y-axis, and origin Continuity: Continuous Boundedness: Bounded Asymptotes: None Maximum r-value: 3

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