1. Converting Equations from Polar Form to Rectangular Form
Sec. 6.4

2. First, remind me of the Coordinate Conversion Equations…
x =
r cos 0
r = 2
x + y 2 2 y
y =
r sin 0
tan 0 = x

3. Now, on with the Examples…
Convert r = 4 sec 0 to rectangular form and identify the graph.
Support your answer graphically.
How did I reach each step???
A vertical line through x = 4!
Check your calculator!

4. Now, on with the Examples…
Convert r = 4 cos 0 to rectangular form and identify the graph.
Support your answer graphically.
CTS!!!
Factor!!!
Conversion Equations
A circle with center (2, 0)
and radius 2

5. More Examples horizontal line
Convert the given polar equation to rectangular form. Identify
the graph, and support your answer graphically.
horizontal line

6. More Examples Circle with center (–2, 0) and radius 2
Convert the given polar equation to rectangular form. Identify
the graph, and support your answer graphically.
Circle with center (–2, 0)
and radius 2

7. More Examples Circle with center (3/2, 0) and radius 3/2
Convert the given polar equation to rectangular form. Identify
the graph, and support your answer graphically.
Circle with center (3/2, 0)
and radius 3/2

8. More Examples Circle with center (2, –2) and radius 2 2
Convert the given polar equation to rectangular form. Identify
the graph, and support your answer graphically.
Circle with center (2, –2)
and radius 2 2

9. Converting Equations
from Rectangular Form
to Polar Form

10. Right in with an example…
Convert the given rectangular equation to polar form. Identify
the graph, and support your answer graphically.
Expanded the binomial!!
Circle with center (1, 0)
and radius 1
Conversion Equations

11. Guided Practice Vertical line
Convert the given rectangular equation to polar form. Identify
the graph, and support your answer graphically.
Vertical line

12. Line with slope –3/4 and y-intercept 1/2
Guided Practice
Convert the given rectangular equation to polar form. Identify
the graph, and support your answer graphically.
Line with slope –3/4 and y-intercept 1/2

13. Guided Practice
Convert the given rectangular equation to polar form. Identify
the graph, and support your answer graphically.

14. Circle with center (3, 2) and radius 13
Guided Practice
Convert the given rectangular equation to polar form. Identify
the graph, and support your answer graphically. OR
Check the graph?
Circle with center (3, 2) and radius 13

15. One more use for polar coordinates…
Radar tracking often gives location in polar coordinates. Suppose
that 2 airplanes are at the same altitude with polar coordinates
of (8 mi, 110 ) and (15 mi, 15 ). How far apart are the airplanes?
First, let’s see a graph…
Next, use the Law of Cosines!!!
The airplanes are about miles apart

16. The ships are about 2968.131 meters apart
Another Example
Using radar, a navy ship locates two enemy ships at polar
coordinates of (5230m, 130 ) and (6721m, 155 ). Find the
distance between the two enemy ships.
The ships are about meters apart