The Polar Coordinate System The Polar Coordinate System is a coordinate plane based on the dimensions r and q.

Points on a Polar Graph A point on a polar coordinate plane is given by the ordered pair, (r, q), where: r = distance from origin to point q = angle in standard position to the point

The Polar Grid

Plotting a Point

More Than One Ordered Pair Can Describe a Point

Negative ‘r’ Values

Name 4 Ordered Pairs

#1: Counter-Clockwise

#2: Clockwise (negative q)

#3: CCW/flipped (neg. r)

#3: CW/flipped (neg. q & neg. r)

Name 4 Ordered Pairs

Try these Plot (3, 120°) Plot (- 5, 210°) Plot (4 , - 90°)

Try these Name three other ordered pairs for the point (5,- 100°).

Basic Polar Graphs We graph Equations in the Polar Coordinate System that are in terms of r and q. We will consider the following: r = k (r = a constant) q = k (q = a constant)

Graph r = k The coordinate, r, tells us how far from the origin to put a point. The equation r = 4 stands for : ‘all the points that are 4 units from the origin’. What would the graph of all these points look like?

r = 4 is a CIRCLE

Graph q = k The coordinate, q, tells us along what angle a point lies. The equation q = 120° stands for : ‘all the points that are along the 120° line’. What would the graph of all these points look like?

q = 120° is a LINE Notice the line is in both quadrants 2 & 4. The points in quadrant 4 are points with q = 120° and a NEGATIVE value for r.

Summary Points in a Polar Grid are given by (r, q) - the values of r and q can be positive or negative. Each point can be given by several different ordered pairs. The polar equation r = k is a circle. The polar equation q = k is a line.