Announcements

1
Announcements

• Test 4 is on Friday (Apr 16).
• Content will cover material through section 5.1
• Do not miss the exammakeup exams are not
  automatic or guaranteed - emergencies and
  university functions only.
• The opportunity to complete HW7, HW8, HW9 Lab7,
  and Lab8 expires on Mar 12.

2
Announcements

• Sample test is posted on course Web site.
• Bring your student ID.
• You can use a calculator, up to a TI-86 or
  equivalent.
• You cant use the book, or your notes.

3
Section 5.1 Polar Coordinates
4
Polar Coordinates
r
 
Pole
Polar axis
5
Comparing Rectangular and Polar Coordinate Systems
Rectangular Coordinates (x, y)
y
Polar Coordinates (r, ?)
r
Origin
?
Polar Axis
x
Pole
6
r
y

x
7
Find polar coordinates of a point whose
rectangular coordinates are (0,3).
Use
8
We have discovered that polar coordinates for the
point are
Are these the only polar coordinates that give us
the point?
9
A point with polar coordinates (r, ?) also can be
represented by either of the following
coordinates (r, ? 2kp) or (-r, ? p
2kp) where k is any integer. Note that the polar
coordinates of the pole are (0, ?), where ? can
be any angle.
10
What are some other polar coordinates for
k (r, ? 2kp) (-r, ? p 2kp)
1 (3, p/2 2p) (-3, p/2 p 2p)
-1 (3, p/2 - 2p) (-3, p/2 p - 2p)
2 (3, p/2 4p) (-3, p/2 p 4p)
-2 (3, p/2 - 4p) (-3, p/2 p - 4p)
11

• Steps for Converting from Rectangular to Polar
  Coordinates
• Plot the point (x, y).
• Find r by computing the distance from the origin
  to (x, y).
• Find ? by first determining the quadrant where
  the point lies, then use one of the following
  formulas

Quadrant I ? tan-1(y/x)
Quadrant II ? p tan-1(y/x)
Quadrant III ? p tan-1(y/x)
Quadrant IV ? tan-1(y/x)
12
Transforming Equations from Polar to Rectangular
Form
When converting an equation from polar to
rectangular form, attempt to algebraically create
the following expressions r2, r cos ?, r sin
? Then use the following facts to convert from
polar to rectangular form r2 x2 y2x r cos
?y r sin ?
Remember
13
Transform r 4 sin ? from polar to rectangular
form and identify its graph.
Standard form of a circle is (x h)2 (y k)2
radius2where (h, k) is the center
r 4 sin ?
rr r(4 sin ?)
r2 4 r sin ?
x2 y2 4y
x2 y2 - 4y 0
x2 (y2 - 4y 4) 0 4
Equation of a circle
x2 (y - 2)2 4
Center (0, 2), radius is 2
14
Transform r 2 from polar to rectangular form.
Circle with center (0, 0) and radius 2