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 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

Try This Write the polar equation of the circle with center (4,0) and radius 4. (Hint: Start with the rectangular equation)

Roses 8 4 petals Polar Roses

Important Idea 10 8 petals Polar Roses

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