The Polar Coordinate System

1
The Polar Coordinate System

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

2
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

3
The Polar Grid
4
Plotting a Point
5
More Than One Ordered Pair Can Describe a Point
6
Negative r Values
7
Name 4 Ordered Pairs
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1 Counter-Clockwise
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2 Clockwise (negative q)
10
3 CCW/flipped (neg. r)
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3 CW/flipped (neg. q neg. r)
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Name 4 Ordered Pairs
13
Try these

• Plot (3, 120)
• Plot (- 5, 210)
• Plot (4 , - 90)
• Plot (- 2 , -165)

14
Try these

• Name three other ordered pairs for the point (5,-
  100).
• Name three other ordered pairs for the point (1,
  200).

15
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)

16
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?
17
r 4 is a CIRCLE
18
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?
19
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.
20
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.