Give 4 different pairs of polar coordinates that correspond to the Cartesian Coordinates (2,2)

Definition A Polar Coordinate System is a method of locating a point (r, ) in a plane where r is a distance from a point called the pole directed at an angle θ measured counterclockwise from a polar axis.

Example r=10 Pole Polar Axis Polar Grid (r,θ )=

r=10 r= ̶ 10 Negative radius means go in the opposite directions Remember to consider the rotation FIRST r=10 r= ̶ 10

Example Find the polar coordinates: (r,θ )=

Example Find the polar coordinates: (r,θ )=

Plot Name the point with three other polar coordinates using

Important Idea Polar coordinates are related to rectangular coordinates as follows: r y θ x

Example Graph: r=6 What about r = ̶ 6?

Example Graph: θ= What about

Some Classic Polar Graphs Example Some Classic Polar Graphs limacon

Example A Classic Polar Graph Spiral of Archimedes

Some Classic Polar Graphs Example Some Classic Polar Graphs 8 petal rose

Use your graphing calculator to graph CARDIOID MODE POL Y= GRAPH

Important Idea 8 4 petals Polar Roses

Important Idea 10 8 petals Polar Roses

Try This Name the angle in rads? Polar Roses

Important Idea What do you observe about the number of petals? The period?

Some Calculus Find the slope of at . Demana text ex 5 p.552

We can write polar equations parametrically where