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P. 776: 3-22 S
P. 776: 23
P. 776: 25-27
P. 776-7: 29, 30, 33
P. 777: 37-44 S
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Instead of defining one coordinate as a function
of the other coordinate, parametric functions
define both coordinates as a function of
another variable, called the parameter.
0
0
6
1
1/4
21
2
1/2
34
3
3/4
45
4
1
54
5
5/4
61
6
3/2
66
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Interestingly, the
representation of a
rectangular equation as a
set of parametric equations
is not unique. Everything
depends on the parameter.
0
0
6
0
6
1
1/4
21
1/2
34
2
1/2
34
1
54
3
3/4
45
3/2
66
4
1
54
2
70
The second set of parametric
equations traces out the
same plane curve as the
first set. It just does so
twice as fast.
Objectives:
1. To evaluate and graph
curves represented by
a set of parametric
curves
2. To rewrite parametric
equations as
rectangular equations
by eliminating the
parameter
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•
•
•
•
Assignment:
P. 776: 3-22 S
P. 776: 23
P. 776: 25-27
P. 776-7: 29, 30, 33
P. 777: 37-44 S
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It is often more convenient to
graph a set of parametric
equations by first converting
them into a rectangular
equation. Then graph the
corresponding rectangular
equation over an
appropriately restricted
domain. This process is
called eliminating the
parameter.
(New Domain)
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For a given set of
parametric equations,
the parameter does
not have to represent
time. It could, for
example, represent an
angle.
Method 1:
For a given set of
parametric equations,
the parameter does
not have to represent
time. It could, for
example, represent an
angle.
Method 2:
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As we have seen, for a given rectangular
equation, its representation as a set of
parametric equations is not unique.
To derive one such representation, simply
choose some parameter and rewrite your
equations using substitution.
•
•
Objectives:
1. To evaluate and graph
curves represented by
a set of parametric
curves
2. To rewrite parametric
equations as
rectangular equations
by eliminating the
parameter
•
•
•
•
•
Assignment:
P. 776: 3-22 S
P. 776: 23
P. 776: 25-27
P. 776-7: 29, 30, 33
P. 777: 37-44 S