JMerrill, 2010
 Coordinate
Conversion
 To convert from polar to rectangular:
 x = r cosθ
 y = r sinθ
 To convert from rectangular to polar:
y
 tanθ = x
 x2 + y2 = r2
 
 2,  53 
There are many ways to represent the point 2, 3 .

2
 2, 3 
 2, 3    2,  53 
(r, )   r,  2n 

When converting from one coordinate
system to the other, we will only use 1
point instead of multiple
representations.
1
2
3
0
3
2
3
There are 3 tests for symmetry, but they don’t
always work, so we’ll use the Quick Test
 For
equations like r = f(sin θ)
• Graph is symmetric to the line y 
 For

2
equations like r = g(cos θ)
• Graph is symmetric to the polar (x) axis
 See
Ex. 2 on page 786—a good use of
sketching using symmetry.
Example:
Find the zeros and the maximum value of r
for the graph of r = 2cos .

2
The maximum value of r is
2. It occurs when  = 0 and
r  0 when
   and 3 .
2
2
2.

1
These are the zeros
2
3
0
of r.
3
2
Copyright © by Houghton Mifflin Company, Inc. All
rights reserved.
Symmetric about the
polar axis
6