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## 6.5

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**6.5**Graphs and Polar Equations**What you’ll learn about**• Polar Curves and Parametric Curves • Symmetry • Analyzing Polar Curves • Rose Curves • Limaçon Curves • Other Polar Curves … and why Graphs that have circular or cylindrical symmetry often have simple polar equations, which is very useful in calculus.**Symmetry**The three types of symmetry figures to be considered will have are: 1. The x-axis (polar axis) as a line of symmetry. 2. The y-axis (the line θ = π/2) as a line of symmetry. 3. The origin (the pole) as a point of symmetry.**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 SymmetryReplaceBy 1. about the x-axis (r,θ) (r,–θ) or (–r, π–θ) 2. about the y-axis (r,θ) (–r,–θ) or (r, π–θ) 3. about the origin (r,θ) (–r,θ) or (r, π+θ)