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61.
If (
r
,
u
) is a solution, so is (
r
,
p
2
u
). Therefore, the curve
is symmetric about the
y
axis. The curve does not have
x
axis or origin symmetry.
62.
If (
r
,
u
) is a solution, so is (
2
r
,
u
). Therefore, the curve is
symmetric about the origin. And if (
r
,
u
) is a solution, so is
(
r
,
2
u
). Therefore, the curve is symmetric about the
x
axis.
And since any curve with
x
axis and origin symmetry also
has
y
axis symmetry, the curve is symmetric about the
y
axis.
63. (a)
Because
r
5
a
sec
u
is equivalent to
r
cos
u
5
a,
which
is equivalent to the Cartesian equation
x
5
a
.
(b)
r
5
a
csc
u
is equivalent to
y
5
a
.
64. (a)
The graph is the same for
n
5
2 and
n
52
2, and in
general, it’s the same for
n
5
2
k
and
n
52
2
k
. The graphs for
n
5
2, 4, and 6 are roses with
4, 8, and 12 “petals” respectively.
The graphs for
n
56
2 and
n
56
6 are shown below.
n
56
2
[
2
3, 3] by [
2
2, 2]
n
56
6
[
2
3, 3] by [
2
2, 2]
(b)
2
p
(c)
The graph is a rose with 2
)
n
)
“petals”.
(d)
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 Spring '08
 GERMAN

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