This preview shows page 1. Sign up to view the full content.
148
Chapter 6
•
Additional Topics
§6.4
Example 6.14
Express the spiral from Figure 6.4.1 in polar coordinates.
Solution:
We will use radians for
θ
. The goal is to ±nd some equation involving
r
and
θ
that describes
the spiral. We see that
θ
=
0
⇒
r
=
1
θ
=
2
π
⇒
r
=
2
θ
=
4
π
⇒
r
=
3
.
.
.
θ
=
2
π
k
⇒
r
=
1
+
k
for
k
=
0,1,2,.
... In fact, that last relation holds for any nonnegative real number
k
(why?). So for
any
θ
≥
0,
θ
=
2
π
k
⇒
k
=
θ
2
π
⇒
r
=
1
+
k
=
1
+
θ
2
π
.
Hence, the spiral can be written as
r
=
1
+
θ
2
π
for
θ
≥
0. The graph is shown in Figure 6.4.5, along
This is the end of the preview. Sign up
to
access the rest of the document.
This note was uploaded on 01/21/2012 for the course MAC 1130 taught by Professor Dr.cheun during the Fall '11 term at FSU.
 Fall '11
 Dr.Cheun
 Calculus, Addition, Polar Coordinates

Click to edit the document details