Polar Coordinates And Complex Numbers Worksheets With Answers - Math 611b Page 12
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50Polar and Rectangular Coordinates (9.3)
1. Write the polar coordinates of the points in the graphs shown.
2. Explain why you have to consider what quadrant a point lies in when converting from rectangular to
polar coordinates.
3. Find the polar coordinates of each point with the given rectangular coordinates.
#
$
2 < 2 B and r
Use 0
0.
− 2
b) ( ! 2, ! 5)
c) (2, ! 2)
f) (4, ! 7)
(
,
2
)
a)
d) (0,1)
e) (3, 8)
4. Find the rectangular coordinates of each point with the given polar coordinates.
a) ( ! 2, 4 B /3)
c) (3, B /2)
b) (2.5, 250°)
d) (4, 210°)
5. Write each rectangular equation in polar form.
c) x = ! 7
2
2
2
2
a) y = 2
b) x
+ y
= 16
d) y = 5
e) x
+ y
= 25
! y
+ (y ! 2)
2
2
2
2
2
2
f) x
+ y
= 2y g) x
= 1
h) x
= 4
6. Write each polar equation in rectangular form.
b) r = ! sec 2
e) 2 = B /3
d) r = ! 3
a) r = 6
c) r = 2
f) r = 2 csc 2
g) r = 3 cos 2
sin 2 2 = 8 i) r( cos 2 + 2 sin 2 ) = 4
2
h) r
7. A surveyor identifies a landmark at the point with polar coordinates (325, 70°). What are the
rectangular coordinates of this point?
12
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