10.3 day 1Polar Coordinates

Greg Kelly, Hanford High School, Richland, Washington

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.

Initial ray

r A polar coordinate pair

determines the location of a point.

,r

1 2 02

r

r a

o

(Circle centered at the origin)

(Line through the origin)

Some curves are easier to describe with polar coordinates:

30o

2

More than one coordinate pair can refer to the same point.

2,30o

2,210o

2, 150o

210o

150o

All of the polar coordinates of this point are:

2,30 360

2, 150 360 0, 1, 2 ...

o o

o o

n

n n

Tests for Symmetry:

x-axis: If (r, ) is on the graph,

r

2cosr

r

so is (r, -).

Tests for Symmetry:

y-axis: If (r, ) is on the graph,

r

2sinr

r

so is (r, -)

or (-r, -).

Tests for Symmetry:

origin: If (r, ) is on the graph,

r

r

so is (-r, ) or (r, +) .

tan

cosr

Tests for Symmetry:

If a graph has two symmetries, then it has all three:

2cos 2r