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Polar Coordinates

- 11.3

What is a coordinate system?

- Wheres Grannys 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

Cartesian from Polar

- Polar from Cartesian

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

Polar Plots

- Are not tales of the far north!
- Are graphs relating r and q
- Example

Try some

- What do the following look like?
- A)
- B)
- C)

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

Other examples.

- 11.3
- 25,37,45,54,63
- Try to graph these using the graphing applet (or

in Maple) - 69 - 74

Areas in Polar Form

- Lets investigate the following

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