1. 9.6 Intro to Polar Coordinates
Greg Kelly, Hanford High School, Richland, Washington

2. A polar coordinate pair
One way to give someone directions is to tell them to go three blocks East and five blocks South.
Another way to give directions is to point and say “Go a half mile in that direction.”
Polar graphing is like the second method of giving directions. Each point is determined by a distance and an angle.
A polar coordinate pair O
determines the location of a point.
Initial ray
(pole)
(polar axis)

3. A Polar Coordinate graph looks similar to the angles on a unit circle:

4. Ex. 1 On your grid paper, plot the following points:
What do you notice about points B and C?

5. All of the polar coordinates of this point are:
With rectangular coordinates, each (x, y) pair has a unique location.
More than one polar coordinate pair can refer to the same point.
All of the polar coordinates of this point are:

6. Coordinate Conversions:
If we make a right triangle using the
polar coordinate, we can say that:

7. Ex. 1 Convert to rectangular:
Ex. 2 Convert to polar:
One possibility:

8. Ex. 3. Graph in your calculator
Ex. 3 Graph in your calculator. Confirm it by converting to rectangular: a)
(This is the set of all points 2 units
away from the pole.)
(Circle at the origin with radius = 2)

9. b)
(The set of all points on the
line that makes an angle of
with the positive x-axis.)
(Line through the origin with a
slope of .)

10. c)
We have a vertical line through 1!

11. Try graphing this on your calculator!