10.5: Polar 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 A polar coordinate pair determines the location of a point.

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. x-axis A polar coordinate pair

is a polar function in which the length r is a function of the angle  Some curves are easier to describe with polar coordinates: …but how to plot such a function…

is a polar function in which the length r is a function of the angle  Some curves are easier to describe with polar coordinates:

is a polar function in which the length r is a function of the angle  Some curves are easier to describe with polar coordinates: …but how can this be?

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. x-axis

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. x-axis But what about this coordinate pair?

is a polar function in which the length r is a function of the angle  Some curves are easier to describe with polar coordinates: …but how can this be?

(Circle centered at the origin) Some curves are easier to describe with polar coordinates: (Try graphing it on your calculator) (Line through the origin whose slope is )

More than one coordinate pair can refer to the same point. All of the polar coordinates of this point are:

Tests for Symmetry: x-axis: If (r,  ) is on the graph,so is (r, -  ).

Tests for Symmetry: y-axis: If (r,  ) is on the graph,so is (r,  -  )or (-r, -  ).

Tests for Symmetry: origin: If ( r,  ) is on the graph,so is (- r,  )or ( r,  +  ).

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

Converting to Cartesian Coordinates Remember the unit circle?

Converting to Cartesian Coordinates Convertto polar coordinates Graph this on your calculators for comparison