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Graphing Polar Equations: A Guide to Notation and Intersection Points

Learn how to graph polar equations on a polar coordinate system, convert between polar and rectangular forms, find intersection points, and use calculators effectively. Practice with examples provided.

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Graphing Polar Equations: A Guide to Notation and Intersection Points

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  1. 10.4 Polar Coordinates & Graphs

  2. Notation Distance Direction

  3. Equations • When you are graphing equations in polar form, you graph them on a polar coordinate system.

  4. Examples

  5. Polar Vs. Rectangular

  6. Converting Between the Two • Some things to remember:

  7. Graphing Polar Curves& Finding Intersection Points • Just use your calculator to get a graph of polar functions. • The only thing you have to worry about (as far as graphing is concerned) is possibly the window settings. • To find the intersection points, you will need to determine when the curves are equal to each other.

  8. Example 1 • Graph the following curves and determine their points of intersection. • Note that if a domain is not given, you can assume it to be [0, 2π]. • First, a graph:

  9. Example 1 (cont.) • Now for their points of intersection: • These curves will intersect for any values of θ that cause the “r” to be the same. • So…

  10. Example 1 (cont.)

  11. Example 2 • Graph the following curves and determine their points of intersection.

  12. Example 2 (cont.)

  13. Homework • Pg. 736 # 1-6, 11-16, 27-33, 35-42 [2 each section]

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