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Polar Coordinates

Polar Coordinates. 11.3. What is a coordinate system?. Where’s Granny’s house? A coordinate system assigns a numerical representation of position of a point space (or the plane). Common systems: Cartesian ‘x-y’ grid Polar Cylindrical Spherical Polar. Cartesian  Polar Coordinates.

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Polar Coordinates

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  1. Polar Coordinates 11.3

  2. What is a coordinate system? • Where’s Granny’s house? • A coordinate system assigns a numerical representation of position of a point space (or the plane). • Common systems: • Cartesian ‘x-y’ grid • Polar • Cylindrical • Spherical Polar

  3. Cartesian  Polar Coordinates Polar from Cartesian Cartesian from Polar

  4. So – why do we need this? • Sometimes the symmetry of the situation makes one coordinate system more “natural” • Sometimes mathematical operations and expressions are simpler in one coordinate system than another • Sometimes unexpected insights emerge when you change coordinate systems • Having a variety of coordinates systems enlarges your “math vocabulary” and allows you to express ideas more clearly

  5. Polar Plots • Are not tales of the far north! • Are graphs relating r and q • Example:

  6. Try some… • What do the following look like? • A) • B) • C)

  7. Tangents to Polar Curves… • How can you find the slope on a polar plot? • Answer – start with and use the conversion fromcartesians to polars • Try this on the previous 3 examples

  8. Other examples…. • 11.3 • 25,37,45,54,63 • Try to graph these using the graphing applet (or in Maple): • 69 - 74

  9. Areas in Polar Form • Let’s investigate the following…

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