Multiple Choice
Identify the
choice that best completes the statement or answers the question.
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1.
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Plot the
point. 
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2.
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Plot the
point. 
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3.
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Plot the
point. ( 4,
-135°)
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4.
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Give the rectangular
coordinates for the point.
(3, 90°)
a. | (0,
3) | c. | ( 3,
0) | b. | ( -3,
0) | d. | (0,
-3) |
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5.
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Give the rectangular
coordinates for the point.
(
-6, 225°)
a. | ( 3 , 3 ) | c. | (
3ð, 3ð) | b. | ( 3 , 3 ) | d. | ( -3 ,
-3 ) |
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6.
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Give the rectangular
coordinates for the point.
(
-4, 0°)
a. | ( 4,
0) | c. | ( 0,
-4) | b. | ( 0, 4) | d. | ( -4, 0) |
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7.
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Give the rectangular
coordinates for the point.
a. | ( -1,
0) | c. | (0,
-1) | b. | ( 1, 0) | d. | (0, 1) |
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8.
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Give the rectangular
coordinates for the point.
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9.
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The rectangular coordinates
of a point are given. Express the point in polar coordinates with  and 
( 3,
3)
a. | ( 3 ,
45°) | c. | ( 3,
90°) | b. | ( 3 , 135°) | d. | ( 3, 45°) |
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10.
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The rectangular coordinates
of a point are given. Express the point in polar coordinates with  and 
( -2,
0)
a. | ( 2,
90°) | c. | ( -2,
180°) | b. | ( 2, 270°) | d. | ( 2, 180°) |
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11.
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The rectangular coordinates
of a point are given. Express the point in polar coordinates with  and 
(0,  )
a. | ( 7,
90°) | c. | ( ,
90°) | b. | ( , 270°) | d. | ( 7, 270°) |
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12.
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The rectangular coordinates
of a point are given. Express the point in polar coordinates with  and 
( ,
- )
a. | ( 6,
225°) | c. | ( ,
135°) | b. | (  , 315°) | d. | (  ,
225°) |
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13.
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The rectangular coordinates
of a point are given. Express the point in polar coordinates with  and 
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14.
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Determine two pairs of polar
coordinates for the point with 0° = è
< 360°.
( 3, -3)
a. | ( 3 , 225°),
( -3 , 45°) | c. | ( 3 , 45°), ( -3 , 225°) | b. | ( 3 , 315°), ( -3 ,
135°) | d. | ( 3 , 135°),
( -3 ,
315°) |
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15.
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Determine two pairs of polar
coordinates for the point with 0° = è
< 360°.
( -2, 0)
a. | ( 2, 90°), ( -2,
270°) | c. | ( 2, 270°), (
-2, 90°) | b. | ( 2, 0°), ( -2, 180°) | d. | ( 2, 180°), ( -2, 0°) |
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16.
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Determine two pairs of polar
coordinates for the point with 0° = è
< 360°.
(0, -  )
a. | ( , 90°),
(-  , 270°) | c. | ( , 0°), (-  , 180°) | b. | ( , 90°), (-  ,
0°) | d. | ( , 270°),
(-  ,
90°) |
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17.
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Determine two pairs of polar
coordinates for the point with 0° = è
< 360°.
( -9, 3 )
a. | ( 6 , 120°),
( -9 , 240°) | c. | ( 6 , 30°), ( -6 , 330°) | b. | ( 6 , 60°), ( -6 ,
300°) | d. | ( 6 , 150°),
( -6 ,
330°) |
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18.
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Determine two pairs of polar
coordinates for the point with 0° = è
< 360°.
( -2 ,
-2 )
a. | ( 4, 225°), ( -4,
45°) | c. | ( 4, 135°), (
-4, 225°) | b. | ( 2 , 225°), ( -2 ,
45°) | d. | ( 2 , 135°),
( -2 ,
225°) |
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19.
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For the given rectangular
equation, give its equivalent polar equation.
10x - y = 3
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20.
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For the given rectangular
equation, give its equivalent polar equation.
2x - 9y = -10
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21.
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Find an equivalent equation
in rectangular coordinates.
r = 10 sin è
a. |  +  = 10x | c. | 
+  = 10y | b. |  =
10x | d. |  =
10y |
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22.
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Find an equivalent equation
in rectangular coordinates.
r = cos è
a. | (x + y)2 =
x | c. | x2 + y2 =
x | b. | x2 + y2 =
y | d. | (x + y)2 = y |
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23.
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Find an equivalent equation
in rectangular coordinates.
r sin è = 10
a. | y = 10x | c. | y = 10 | b. | x = 10y | d. | x = 10 |
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24.
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Find an equivalent equation
in rectangular coordinates.
r(cos è - sin è) = 3
a. | x - y =
3 | c. |  (x - y)
= 3 | b. | x - y = 9 | d. | x + y = 3 |
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25.
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Find an equivalent equation
in rectangular coordinates.
r - 6 sin è = 4 cos
è
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26.
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The graph of a polar
equation is given. Select the polar equation for the graph.
a. | r =
-2 | c. | r = -4 sin
è | b. | r = -4 cos è | d. | r sin è =
-2 |
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27.
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The graph of a polar
equation is given. Select the polar equation for the graph.
a. | r = 4 cos
è | c. | r = 4 sin
è | b. | r = 2 + cos è | d. | r = 2 + sin è |
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28.
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The graph of a polar
equation is given. Select the polar equation for the graph.
a. | r = 5 sin( 5è) | c. | r = 5 + cos(
5è) | b. | r = 5 cos( 5è) | d. | r = 5 |
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29.
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Graph the polar equation for
è in [0°, 360°).
r = 4 + 4
sin è
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30.
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Graph the polar equation for
è in [0°, 360°).
r = 2 - cos
è
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31.
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Graph the polar equation for
è in [0°, 360°).
r = 8 cos
7è
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32.
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Graph the polar equation for
è in [0°, 360°).
r = 5 (cos
è + cos 2è)
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33.
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The graph of r =
aè in polar coordinates is an example of the spiral of
Archimedes. With your calculator set to radian mode, use the given value of a and interval of
è to graph the spiral in the window specified.
a = 3, 0 = è = 2ð,
[-20, 20] by [-20, 20]
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34.
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The graph of r =
aè in polar coordinates is an example of the spiral of
Archimedes. With your calculator set to radian mode, use the given value of a and interval of
è to graph the spiral in the window specified.
a = -0.5, -ð = è =
4ð, [-6, 6] by [-6, 6]
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35.
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Find the polar coordinates
of the point(s) of intersection of the given curves for 0 = è
< 2ð.
r = 10 + 3 sin
è, r = 10 + 3 cos è
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36.
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Find the polar coordinates
of the point(s) of intersection of the given curves for 0 = è
< 2ð.
r = 3 + cos
è, r = 3 - sin è
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37.
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Given that the polar equation r
=  models the orbits of the planets, estimate
the smallest possible distance between Earth, for which  and 
and Venus, for which  and 
a. | About 2 astronomical
units | c. | Zero astronomical
units | b. | About 0.2 astronomical units | d. | About 0.4 astronomical units |
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38.
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Given that the polar equation r
=  models the orbits of the planets about the
sun, estimate the closest approach of a planet for which  and 
to the sun.
a. | 67 astronomical
units | c. | 7 astronomical
units | b. | 13 astronomical units | d. | 22 astronomical units |
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