Deck 3: Radian Measure
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Deck 3: Radian Measure
1
Find θ , if
and
and θ in QIV
A)300
B)60
C)120
D)45
E)240


A)300

B)60

C)120

D)45

E)240

300 

2
Find the exact value of
.
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)


3
Find the exact value of sin 300º.
A)
B)
C)
D)
E)
A)

B)

C)

D)

E)


4
Use a calculator to find
Please round the answer to the nearest ten-thousandth.
A)-1.2386
B)-1.2258
C)-1.2458
D)-1.2257
E)-1.2558

A)-1.2386
B)-1.2258
C)-1.2458
D)-1.2257
E)-1.2558
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5
Use a calculator to find
Please round the answer to the nearest thousandth.
A)0.989
B)0.956
C)0.986
D)0.936
E)0.958

A)0.989
B)0.956
C)0.986
D)0.936
E)0.958
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6
Use a calculator to find θ to the nearest tenth of a degree, if
and
with θ in QIII
A)201.3º
B)200.1 º
C)196.8 º
D)194.8 º
E)197.8 º


A)201.3º
B)200.1 º
C)196.8 º
D)194.8 º
E)197.8 º
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7
Use a calculator to find
Please round the answer to the nearest ten-thousandth.
A)0.9064
B)0.9063
C)0.8843
D)0.8863
E)0.9363

A)0.9064
B)0.9063
C)0.8843
D)0.8863
E)0.9363
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8
Find θ , if
and
and θ in QI
A)60
B)120
C)240
D)45
E)300


A)60

B)120

C)240

D)45

E)300

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9
Use a calculator to find θ to the nearest tenth of a degree, if
and
with θ in QII
A)127.5
B)130.0
C)126.5
D)124.2
E)129.5


A)127.5

B)130.0

C)126.5

D)124.2

E)129.5

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10
Draw the following angle in standard position and then name the reference angle.
A)
B)
C)

D)

E)


A)


B)


C)


D)


E)


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11
Use a calculator to find
Please round the answer to the nearest ten-thousandth.
A)-5.3530
B)-5.3960
C)-5.3863
D)-5.4360
E)-5.3860

A)-5.3530
B)-5.3960
C)-5.3863
D)-5.4360
E)-5.3860
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12
Find θ , if
and
and θ in QI
A)210
B)30
C)120
D)45
E)300


A)210

B)30

C)120

D)45

E)300

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13
Use a calculator to find θ to the nearest tenth of a degree, if
and
with θ in QII
A)103.5
B)104.7
C)107.0
D)108.0
E)110.0


A)103.5

B)104.7

C)107.0

D)108.0

E)110.0

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14
Use a calculator to find θ to the nearest tenth of a degree, if
and
with θ in QIII
A)217.5
B)219.8
C)218.8
D)216.3
E)216.8


A)217.5

B)219.8

C)218.8

D)216.3

E)216.8

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15
Use a calculator to find
Please round the answer to the nearest thousandth.

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16
Use a calculator to find
Please round the answer to the nearest ten-thousandth.
A)-0.7893
B)-0.7563
C)-0.7863
D)-0.7463
E)-0.7562

A)-0.7893
B)-0.7563
C)-0.7863
D)-0.7463
E)-0.7562
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17
Find the exact value of
.
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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18
Find θ , if
and
with θ in QIV
A)330
B)300
C)240
D)120
E)45


A)330

B)300

C)240

D)120

E)45

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19
Draw the following angle in standard position and then name the reference angle.
A)
B)
C)

D)

E)


A)


B)


C)


D)


E)


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20
Find the exact value of cos 135º.
A)
B)
C)
D)
E)
A)

B)

C)

D)

E)

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21
Use a calculator to find
Please round the answer to the nearest ten-thousandth.

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22
Convert to radian measure using exact values. θ = 340°
A)
B)
C)
D)
E)
A)

B)

C)

D)

E)

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23
Use a calculator to find tan 143.8°. Please round the answer to the nearest ten-thousandth.
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24
Use a calculator to find θ to the nearest tenth of a degree, if
and
with θ in QIII
__________ 




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25
Find the radian measure of angle θ , if θ is a central angle in a circle of radius r , and θ cuts off an arc of length s .
cm,
cm
A)
B)4
C)
D)
E)5


A)

B)4
C)

D)

E)5
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26
Find the exact value of
.

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27
Find the exact value of
.

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28
Use a calculator to find θ to the nearest tenth of a degree, if
and
with θ in QII
__________°



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29
Find θ , if
and
and θ in QIV
__________°



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30
Use a calculator to find θ to the nearest tenth of a degree, if
and
with θ in QII
__________°



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31
Find the radian measure of angle θ , if θ is a central angle in a circle of radius r , and θ cuts off an arc of length s . r = 4 inches, s = 20 inches
A)5
B)6
C)2
D)3
E)1
A)5
B)6
C)2
D)3
E)1
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32
Find θ , if
and
with θ in QI
__________°



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33
Find the exact value of
Express your answer in simplified form. Do not convert to decimal form.

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34
Find the exact value of
.

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35
Find θ , if
and
and θ in QIII
__________ °



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36
Use a calculator to find θ to the nearest tenth of a degree, if
and
with θ in QIII
__________°



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37
Name the reference angle in both degrees and radians. θ = 170°
A)
B)
C)
D)
E)
A)

B)

C)

D)

E)

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38
Use a calculator to find
Please round the answer to the nearest ten-thousandth.

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39
Use a calculator to find
Please round the answer to the nearest ten-thousandth.

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40
Two cities are approximately 600 miles apart on the surface of the earth. Assuming that the radius of the earth is 4,000 miles, find the radian measure of the central angle with its vertex at the center of the earth that has one city on one side and another one on the other side.
a = 600 miles
A)0.14 radians
B)0.135 radians
C)0.15 radians
D)0.145 radians
E)0.13 radians

A)0.14 radians
B)0.135 radians
C)0.15 radians
D)0.145 radians
E)0.13 radians
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41
Through how many radians does the minute hand of a clock turn during a 5-minute period?
A)
B)
C)
D)
E)
A)

B)

C)

D)

E)

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42
Give the exact value of
.

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43
Label the reference angle in both degrees and radians.
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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44
Give the exact value of
.
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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45
Evaluate the expression when x is
. Use exact values. 3 cos 6 x

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46
Give the exact value of
.

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47
Find the radian measure of angle θ , if θ is a central angle in a circle of radius r , and θ cuts off an arc of length s .
cm,
cm
θ = __________ radians


θ = __________ radians
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48
Through how many radians does the minute hand of a clock turn during a 6-minute period?
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49
For the following expression, find the value of y that corresponds to each value of x , then write your results as ordered pairs ( x, y ).
for 


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50
Give the exact value of
.
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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51
Give the exact value of
.

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52
Two cities are approximately 550 miles apart on the surface of the earth. Assuming that the radius of the earth is 4,000 miles, find the radian measure of the central angle with its vertex at the center of the earth that has one city on one side and another one on the other side.
a = 550 __________ radians

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53
Evaluate the expression when x is
. Use exact values. 7 cos 3 x
A)0
B)7
C)3
D)2
E)-3

A)0
B)7
C)3
D)2
E)-3
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54
For the following expression, find the value of y that corresponds to each value of x , then write your results as ordered pairs ( x, y ).
for
A)
,
,
,
, 
B)
,
,
,
, 
C)
,
,
,
, 
D)
,
,
,
, 
E)
,
,
,
, 


A)





B)





C)





D)





E)





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55
Give the exact value of
.
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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56
Use the unit circle to find the six trigonometric functions of 240°.
A)
B)
C)
D)
E)
A)

B)

C)

D)

E)

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57
Convert to degree measure.
A)170°
B)110°
C)135°
D)140°
E)150°

A)170°
B)110°
C)135°
D)140°
E)150°
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58
Use a calculator to convert 100°10' to radians. Round your answer to the nearest hundredth. (First convert to decimal degrees, then multiply by the appropriate conversion factor to convert to radians.)
A)1.77
B)1.75
C)1.71
D)1.81
E)1.83
A)1.77
B)1.75
C)1.71
D)1.81
E)1.83
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59
Find the radian measure of angle θ , if θ is a central angle in a circle of radius r , and θ cuts off an arc of length s .
r = 5 inches, s = 25 inches
θ = __________ radians
r = 5 inches, s = 25 inches
θ = __________ radians
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60
Use a calculator to convert 150°50' to radians. Round your answer to the nearest hundredth. (First convert to decimal degrees, then multiply by the appropriate conversion factor to convert to radians.)__________ radians
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61
Graph the unit circle using parametric equations with your calculator set to degree mode. Use a scale of 5. Trace the circle to find the sine and cosine of the angle to the nearest ten-thousandth. 225°
A)
B)
C)
D)
E)
A)

B)

C)

D)

E)

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62
Graph the unit circle using parametric equations with your calculator set to radian mode. Use a scale of
. Trace the circle to find all values of t between 0 and 2 π satisfying the following statement. Round your answers to the nearest ten-thousandth.
__________



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63
If we start at the point (1, 0)and travel once around the unit circle, we travel a distance of 2 π units and arrive back where we started at the point (1, 0). If we continue around the unit circle a second time, we will repeat all the values of x and y that occurred during our first trip around. Use this discussion to evaluate the expression.
A)
B)
C)
D)-1
E)1

A)

B)

C)

D)-1
E)1
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64
Graph the unit circle using parametric equations with your calculator set to degree mode. Use a scale of 5. Trace the circle to find all values of t between 0° and 360° satisfying the statement.
__________


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65
Graph the unit circle using parametric equations with your calculator set to radian mode. Use a scale of
. Trace the circle to find all values of t between 0 and 2 π satisfying the following statement. Round your answers to the nearest ten-thousandth.
A)t = 0.5236, 2.8338
B)t = 0.5236, 2.618
C)t = 0.647, 2.8338
D)t = 2.618, 0.647
E)t = 0.5236, 0.647


A)t = 0.5236, 2.8338
B)t = 0.5236, 2.618
C)t = 0.647, 2.8338
D)t = 2.618, 0.647
E)t = 0.5236, 0.647
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66
Use the unit circle to find all values of θ between 0 and 2 π for which
.
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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67
Graph the unit circle using parametric equations with your calculator set to radian mode. Use a scale of
. Trace the circle to find the sine and cosine of
to the nearest ten-thousandth.
A)
B)
C)
D)
E)


A)

B)

C)

D)

E)

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68
Use the unit circle to find the six trigonometric functions of
.
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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69
Use the unit circle to find the six trigonometric functions of
.
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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70
Use the unit circle to find all values of θ between 0 and 2 π for which
.

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71
Graph the unit circle using parametric equations with your calculator set to degree mode. Use a scale of 5. Trace the circle to find all values of t between 0° and 360° satisfying the statement.
A)55°, 155°
B)60°, 300°
C)60°, 150°
D)210°, 150°
E)210°, 300°

A)55°, 155°
B)60°, 300°
C)60°, 150°
D)210°, 150°
E)210°, 300°
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72
If angle θ is in standard position and intersects the unit circle at
find
and
.
A)
B)
C)
D)
E)



A)

B)

C)

D)

E)

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73
Use the unit circle to find all values of θ between 0 and 2 π for which
.

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74
If we start at the point (1, 0)and travel once around the unit circle, we travel a distance of 2 π units and arrive back where we started at the point (1, 0). If we continue around the unit circle a second time, we will repeat all the values of x and y that occurred during our first trip around. Use this discussion to evaluate the expression. 

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75
Use the unit circle to find all values of θ between 0 and 2 π for which
.

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76
Use the unit circle to find all values of θ between 0 and 2 π for which
.
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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77
Graph the unit circle using parametric equations with your calculator set to radian mode. Use a scale of
. Trace the circle to find the sine and cosine of
to the nearest ten-thousandth.
__________
__________




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78
Use the unit circle to find all values of θ between 0 and 2 π for which
.

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79
Graph the unit circle using parametric equations with your calculator set to degree mode. Use a scale of 5. Trace the circle to find the sine and cosine of the angle to the nearest ten-thousandth.
265°
__________
__________
265°


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80
Graph the unit circle using parametric equations with your calculator set to degree mode. Use a scale of 5. Trace the circle to find all values of t between 0° and 360° satisfying the statement.
A)125°, 305°
B)140°, 315°
C)140°, 310°
D)135°, 310°
E)135°, 315°

A)125°, 305°
B)140°, 315°
C)140°, 310°
D)135°, 310°
E)135°, 315°
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