1. Polar Coordinates and Graphing
Section 10.5a

2. Polar Coordinates
To define polar coordinates, we first fix an origin O (called
the pole) and an initial ray from O. Then each point P can
be located by assigning to it a polar coordinate pair :
Directed distance
from O to P
Directed angle from
initial ray to ray OP
Origin (Pole) O
Initial ray

3. Polar Coordinates
Important note: The polar coordinates for any given point
are not unique!!!
Example: Plot the given point, and find two other sets of
polar coordinates that define the point.
Origin
(Pole) O
Initial ray

4. Guided Practice
Plot the points with the given polar coordinates and find
their Cartesian coordinates.
Cartesian coordinates: y x

5. Guided Practice
Plot the points with the given polar coordinates and find
their Cartesian coordinates.
Cartesian coordinates: y x

6. Guided Practice
Plot the points with the given Cartesian coordinates and
find two sets of polar coordinates for each.
Polar coordinates: y x

7. Guided Practice
Plot the points with the given Cartesian coordinates and
find two sets of polar coordinates for each. y
Polar coordinates: x

8. Polar Graphing Equation Polar Graph Circle of radius centered at
Line through making an angle with the
initial ray
Examples:
and are equations for the circle of radius 1
centered at : O x

9. Polar Graphing Equation Polar Graph Circle of radius centered at
Line through making an angle with the
initial ray
Examples:
, , and are equations
for the line: O x

10. Guided Practice
Graph the set of points whose polar coordinates satisfy
the given conditions. y x

11. Guided Practice
Graph the set of points whose polar coordinates satisfy
the given conditions.
and y x

12. Guided Practice
Graph the set of points whose polar coordinates satisfy
the given conditions.
and y x

13. Guided Practice
Graph the set of points whose polar coordinates satisfy
the given conditions.
and y x

14. Guided Practice
Graph the set of points whose polar coordinates satisfy
the given conditions. y x