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Sullivan Algebra and Trigonometry: Section 10.2

Sullivan Algebra and Trigonometry: Section 10.2. Objectives of this Section Graph and Identify Polar Equations by Converting to Rectangular Coordinates Test Polar Equations for Symmetry Graph Polar Equations by Plotting Points.

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Sullivan Algebra and Trigonometry: Section 10.2

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  1. Sullivan Algebra and Trigonometry: Section 10.2 • Objectives of this Section • Graph and Identify Polar Equations by Converting to Rectangular Coordinates • Test Polar Equations for Symmetry • Graph Polar Equations by Plotting Points

  2. An equation whose variables are polar coordinates is called a polar equation. The graph of a polar equation consists of all points whose polar coordinates satisfy the equation.

  3. Identify and graph the equation: r = 2 Circle with center at the pole and radius 2.

  4. Let a be a nonzero real number, the graph of the equation is a horizontal line a units above the pole if a> 0 and units below the pole if a< 0.

  5. Let a be a nonzero real number, the graph of the equation is a vertical line a units to the right of the pole if a> 0 and units to the left of the pole if a< 0.

  6. Let a be a positive real number. Then, Circle: radius a; center at (0, a) in rectangular coordinates. Circle: radius a; center at (0, -a) in rectangular coordinates.

  7. Let a be a positive real number. Then, Circle: radius a; center at (a, 0) in rectangular coordinates. Circle: radius a; center at (-a, 0) in rectangular coordinates.

  8. Symmetry with Respect to the Polar Axis (x-axis):

  9. Symmetry with Respect to the Line (y-axis)

  10. Symmetry with Respect to the Pole (Origin):

  11. Tests for Symmetry Symmetry with Respect to the Polar Axis (x-axis):

  12. Tests for Symmetry Symmetry with Respect to the Line (y-axis):

  13. Tests for Symmetry Symmetry with Respect to the Pole (Origin):

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