Understanding Polar Coordinates in Mathematics

Polar coordinates provide an alternative way to plot points using a directed angle and distance from the origin. This system involves radius (distance) and angle measurements, allowing for multiple representations of points. Graphing polar coordinates, converting between polar and rectangular coordinates, and exploring various representations are key aspects of working with this coordinate system.

• Mathematics
• Polar Coordinates
• Graphing
• Conversions
• Coordinate Systems

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1. 10.7 Polar Coordinates 10.7 Polar Coordinates

2. Definitions/ Characteristics Definitions/ Characteristics Polar coordinates: a 2ndway to plot points using a directed angle and a directed distance. Written as: (r, ) where r is the radius (distance) and is the angle Uses concentric circles and angles in standard position Each point can have may different polar coordinates to represent it (unlike rectangular coordinates- which only have 1)

4. Graphing Polar Coordinates Graphing Polar Coordinates

5. Graphing Polar Coordinates Graphing Polar Coordinates

6. Multiple Representations of Polar Coordinates Multiple Representations of Polar Coordinates

7. Multiple Representations of Polar Coordinates Multiple Representations of Polar Coordinates

8. Multiple Representations of Polar Coordinates Multiple Representations of Polar Coordinates

9. Conversions Conversions

10. Converting: Polar to Rectangular Coordinates Converting: Polar to Rectangular Coordinates

11. Converting: Polar to Rectangular Coordinates Converting: Polar to Rectangular Coordinates

12. Converting: Rectangular to Polar Coordinates Converting: Rectangular to Polar Coordinates

13. Converting: Rectangular to Polar Coordinates Converting: Rectangular to Polar Coordinates

14. Converting Equations: Rectangular to Polar Converting Equations: Rectangular to Polar Steps: Substitute for x and y Solve for r

15. Converting Equations: Rectangular to Polar Converting Equations: Rectangular to Polar

16. Converting Equations: Polar to Rectangular Converting Equations: Polar to Rectangular Must think to solve these- manipulate the equation to match with one of the four equations used to convert points 2.) ? =? 3.) ? = ???? 1.) r = 2 3

17. More examples ? 4 5.) ? = 6.) ? = ???? 4.) r = 1

18. Practice problems Practice problems Pg 783 # 1-4, 6, 10-14 even, 18-24 even, 34-42 even, 50-56 even

19. HMWK Pg 783 # 9-13 odd, 17-23 odd, 33-41 odd, 49-55 odd