Diagram

Unit 7 - Vectors

Polar Coordinates

Polar Coordinate System · To form the polar coordinate system in a plane fix a point O, call is the pole or the origin while the initial ray is the polar axis.

· Each point P in the plane can be assigned the polar coordinate

· directed distance = directed angle =

Diagram:

Unit 7 - Vectors

Plotting Points Using polar graph paper, plot each point.

1)

2)

Polar Coordinates

Unit 7 - Vectors

Polar Coordinates

3)

In a rectangular coordinate system every point has _______________.

In the polar system, that is true - because it is based on rotation - there can be multiple representations of the same polar location.

Unit 7 - Vectors

Polar Coordinates

Plot the given point and find 3 additional points to represent that location given the domain

4)

5. Plot the following points on the graph :

Unit 7 - Vectors

Polar Coordinates

5. Graph each of the polar equations

Polar Coordinates and Rectangular Coordinates Polar coordinates and rectangular coordinates are related in this way:

Rectangular

Polar

You can easily convert one to the other.

Unit 7 - Vectors

Polar Coordinates

Relationships

Convert from Polar to Rectangular

1)

Unit 7 - Vectors

Polar Coordinates

2)

3)

Unit 7 - Vectors

Polar Coordinates

Convert from Rectangular to Polar 4)

5)

Unit 7 - Vectors

Polar Coordinates

6)