Deck 6: Analytic Trigonometry
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Deck 6: Analytic Trigonometry
1
If
, use trigonometric substitution to write
as a trigonometric function of , where
.
A)
B)
C)
D)
E)



A)

B)

C)

D)

E)


2
Which of the following is equivalent to the given expression? 
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)


3
Find the exact value of the given expression using a sum or difference formula. 
A)
B)
C)
D)

A)

B)

C)

D)


4
Use a graphing utility to approximate the solutions (to three decimal places) of the given equation in the interval
. 
A)
B)
C)
D)
E)


A)

B)

C)

D)

E)

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5
Find the exact value of the given expression using a sum or difference formula. 
A)
B)
C)
D)

A)

B)

C)

D)

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6
Write the given expression as an algebraic expression. 
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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7
Multiply; then use fundamental identities to simplify the expression below and determine which of the following is not equivalent. 
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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8
Find the exact solutions of the given equation in the interval
. 
A)
B)
C)
D)
E)


A)

B)

C)

D)

E)

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9
Write the given expression as the cosine of an angle. 
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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10
Use fundamental identities to simplify the expression below and then determine which of the following is not equivalent. 
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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Unlock Deck
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11
If
, use trigonometric substitution to write
as a trigonometric function of , where
.
A)
B)
C)
D)
E)



A)

B)

C)

D)

E)

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Unlock Deck
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12
Write the given expression as the sine of an angle. 
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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Unlock Deck
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13
Use a graphing utility to approximate the solutions (to three decimal places) of the given equation in the interval
. 
A)
B)
C)
D)
E)


A)

B)

C)

D)

E)

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Unlock for access to all 150 flashcards in this deck.
Unlock Deck
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14
Find the exact value of the given expression. 
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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Unlock Deck
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15
Solve the multiple-angle equation. 
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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Unlock Deck
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16
Find the exact value of the given expression. 
A)
B)
C)
D)

A)

B)

C)

D)

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Unlock Deck
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17
Use the cofunction identities to evaluate the expression below without the aid of a calculator. 
A) 2
B) 0
C) 1
D)
E) -1

A) 2
B) 0
C) 1
D)

E) -1
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18
Find the exact value of the given expression. 
A)
B)
C)
D)

A)

B)

C)

D)

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19
Rewrite
as a single logarithm and then simplify the result.
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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20
Find the exact value of
given that
and
. (Both u and v are in Quadrant II.)
A)
B)
C)
D)
E)



A)

B)

C)

D)

E)

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Unlock Deck
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21
Use the figure below to find the exact value of the given trigonometric expression.
5 12
(figure not necessarily to scale)
A)
B)
C)
D)
E)


(figure not necessarily to scale)
A)

B)

C)

D)

E)

Unlock Deck
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Unlock Deck
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22
If
, use trigonometric substitution to write
as a trigonometric function of , where
.
A)
B)
C)
D)
E)



A)

B)

C)

D)

E)

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Unlock Deck
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23
Find the exact value of the given expression. 
A)
B)
C)
D)

A)

B)

C)

D)

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Unlock Deck
k this deck
24
Which of the following is equivalent to the given expression? 
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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Unlock Deck
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25
Solve the multiple-angle equation. 
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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Unlock Deck
k this deck
26
Find the exact value of the given expression. 
A)
B)
C)
D)

A)

B)

C)

D)

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Unlock Deck
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27
Multiply; then use fundamental identities to simplify the expression below and determine which of the following is not equivalent. 
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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Unlock for access to all 150 flashcards in this deck.
Unlock Deck
k this deck
28
Find the exact value of the given expression using a sum or difference formula. 
A)
B)
C)
D)

A)

B)

C)

D)

Unlock Deck
Unlock for access to all 150 flashcards in this deck.
Unlock Deck
k this deck
29
Write the given expression as the cosine of an angle. 
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

Unlock Deck
Unlock for access to all 150 flashcards in this deck.
Unlock Deck
k this deck
30
Find the exact solutions of the given equation in the interval
. 
A)
B)
C)
D)
E)


A)

B)

C)

D)

E)

Unlock Deck
Unlock for access to all 150 flashcards in this deck.
Unlock Deck
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31
If
, use trigonometric substitution to write
as a trigonometric function of , where
.
A)
B)
C)
D)
E)



A)

B)

C)

D)

E)

Unlock Deck
Unlock for access to all 150 flashcards in this deck.
Unlock Deck
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32
Use a graphing utility to approximate the solutions (to three decimal places) of the given equation in the interval
. 
A)
B)
C)
D)
E)


A)

B)

C)

D)

E)

Unlock Deck
Unlock for access to all 150 flashcards in this deck.
Unlock Deck
k this deck
33
Use the cofunction identities to evaluate the expression below without the aid of a calculator. 
A) -1
B) 0
C) 1
D)
E) 2

A) -1
B) 0
C) 1
D)

E) 2
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Unlock Deck
k this deck
34
Use the half-angle formulas to determine the exact value of the given trigonometric expression. 
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

Unlock Deck
Unlock for access to all 150 flashcards in this deck.
Unlock Deck
k this deck
35
Use the product-to-sum formula to write the given product as a sum or difference. 
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

Unlock Deck
Unlock for access to all 150 flashcards in this deck.
Unlock Deck
k this deck
36
Rewrite
as a single logarithm and then simplify the result.
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

Unlock Deck
Unlock for access to all 150 flashcards in this deck.
Unlock Deck
k this deck
37
Find the exact value of the given expression using a sum or difference formula. 
A)
B)
C)
D)

A)

B)

C)

D)

Unlock Deck
Unlock for access to all 150 flashcards in this deck.
Unlock Deck
k this deck
38
Find all solutions of the given equation in the interval
. 
A)
B)
C)
D)
E)


A)

B)

C)

D)

E)

Unlock Deck
Unlock for access to all 150 flashcards in this deck.
Unlock Deck
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39
Use a graphing utility to approximate the solutions (to three decimal places) of the given equation in the interval
. 
A)
B)
C)
D)
E)


A)

B)

C)

D)

E)

Unlock Deck
Unlock for access to all 150 flashcards in this deck.
Unlock Deck
k this deck
40
Use fundamental identities to simplify the expression below and then determine which of the following is not equivalent. 
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

Unlock Deck
Unlock for access to all 150 flashcards in this deck.
Unlock Deck
k this deck
41
Find the exact solutions of the given equation in the interval
. 
A)
B)
C)
D)
E)


A)

B)

C)

D)

E)

Unlock Deck
Unlock for access to all 150 flashcards in this deck.
Unlock Deck
k this deck
42
Use a graphing utility to approximate the solutions (to three decimal places) of the given equation in the interval
. 
A)
B)
C)
D)
E)


A)

B)

C)

D)

E)

Unlock Deck
Unlock for access to all 150 flashcards in this deck.
Unlock Deck
k this deck
43
Which of the following is equivalent to the given expression? 
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

Unlock Deck
Unlock for access to all 150 flashcards in this deck.
Unlock Deck
k this deck
44
Use a graphing utility to approximate the solutions (to three decimal places) of the given equation in the interval
. 
A)
B)
C)
D)
E)


A)

B)

C)

D)

E)

Unlock Deck
Unlock for access to all 150 flashcards in this deck.
Unlock Deck
k this deck
45
Use fundamental identities to simplify the expression below and then determine which of the following is not equivalent. 
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

Unlock Deck
Unlock for access to all 150 flashcards in this deck.
Unlock Deck
k this deck
46
Rewrite
as a single logarithm and then simplify the result.
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

Unlock Deck
Unlock for access to all 150 flashcards in this deck.
Unlock Deck
k this deck
47
Find the exact solutions of the given equation in the interval
. 
A)
B)
C)
D)
E)


A)

B)

C)

D)

E)

Unlock Deck
Unlock for access to all 150 flashcards in this deck.
Unlock Deck
k this deck
48
Write the given expression as the sine of an angle. 
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

Unlock Deck
Unlock for access to all 150 flashcards in this deck.
Unlock Deck
k this deck
49
Use the half-angle formulas to determine the exact value of the given trigonometric expression. 
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

Unlock Deck
Unlock for access to all 150 flashcards in this deck.
Unlock Deck
k this deck
50
If
, use trigonometric substitution to write
as a trigonometric function of , where
.
A)
B)
C)
D)
E)



A)

B)

C)

D)

E)

Unlock Deck
Unlock for access to all 150 flashcards in this deck.
Unlock Deck
k this deck
51
Use the cofunction identities to evaluate the expression below without the aid of a calculator. 
A) 1
B) 2
C) -1
D) 0
E)

A) 1
B) 2
C) -1
D) 0
E)

Unlock Deck
Unlock for access to all 150 flashcards in this deck.
Unlock Deck
k this deck
52
Find the exact value of the given expression. 
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

Unlock Deck
Unlock for access to all 150 flashcards in this deck.
Unlock Deck
k this deck
53
Write the given expression as an algebraic expression. 
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

Unlock Deck
Unlock for access to all 150 flashcards in this deck.
Unlock Deck
k this deck
54
Find all solutions of the given equation in the interval
. 
A)
B)
C)
D)
E)


A)

B)

C)

D)

E)

Unlock Deck
Unlock for access to all 150 flashcards in this deck.
Unlock Deck
k this deck
55
Use the figure below to find the exact value of the given trigonometric expression.
5 12
(figure not necessarily to scale)
A)
B)
C)
D)
E)


(figure not necessarily to scale)
A)

B)

C)

D)

E)

Unlock Deck
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Unlock Deck
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56
Multiply; then use fundamental identities to simplify the expression below and determine which of the following is not equivalent. 
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

Unlock Deck
Unlock for access to all 150 flashcards in this deck.
Unlock Deck
k this deck
57
If
, use trigonometric substitution to write
as a trigonometric function of F , where
.
A)
B)
C)
D)
E)



A)

B)

C)

D)

E)

Unlock Deck
Unlock for access to all 150 flashcards in this deck.
Unlock Deck
k this deck
58
Use the product-to-sum formula to write the given product as a sum or difference. 
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

Unlock Deck
Unlock for access to all 150 flashcards in this deck.
Unlock Deck
k this deck
59
Find the exact value of
given that
and
. (Both u and v are in Quadrant II.)
A)
B)
C)
D)
E)



A)

B)

C)

D)

E)

Unlock Deck
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Unlock Deck
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60
Solve the multiple-angle equation. 
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

Unlock Deck
Unlock for access to all 150 flashcards in this deck.
Unlock Deck
k this deck
61
Find the exact solutions of the given equation in the interval
. 
A)
B)
C)
D)
E)


A)

B)

C)

D)

E)

Unlock Deck
Unlock for access to all 150 flashcards in this deck.
Unlock Deck
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62
Which of the following is equivalent to the given expression? 
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

Unlock Deck
Unlock for access to all 150 flashcards in this deck.
Unlock Deck
k this deck
63
Find all solutions of the given equation in the interval
. 
A)
B)
C)
D)
E)


A)

B)

C)

D)

E)

Unlock Deck
Unlock for access to all 150 flashcards in this deck.
Unlock Deck
k this deck
64
Find the exact value of the given expression. 
A)
B)
C)
D)

A)

B)

C)

D)

Unlock Deck
Unlock for access to all 150 flashcards in this deck.
Unlock Deck
k this deck
65
Find the exact value of
given that
and
. (Both u and v are in Quadrant II.)
A)
B)
C)
D)
E)



A)

B)

C)

D)

E)

Unlock Deck
Unlock for access to all 150 flashcards in this deck.
Unlock Deck
k this deck
66
Use a graphing utility to determine which of the trigonometric functions is equal to the following expression. 
A)
B)
C)
D)
E)
4

A)

B)

C)

D)

E)

Unlock Deck
Unlock for access to all 150 flashcards in this deck.
Unlock Deck
k this deck
67
Use the figure below to find the exact value of the given trigonometric expression.
8 15
(figure not necessarily to scale)
A)
B)
C)
D)
E)


(figure not necessarily to scale)
A)

B)

C)

D)

E)

Unlock Deck
Unlock for access to all 150 flashcards in this deck.
Unlock Deck
k this deck
68
Find the exact value of the given expression using a sum or difference formula. 
A)
B)
C)
D)

A)

B)

C)

D)

Unlock Deck
Unlock for access to all 150 flashcards in this deck.
Unlock Deck
k this deck
69
Write the given expression as the cosine of an angle. 
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

Unlock Deck
Unlock for access to all 150 flashcards in this deck.
Unlock Deck
k this deck
70
If
, use trigonometric substitution to write
as a trigonometric function of , where
.
A)
B)
C)
D)
E)



A)

B)

C)

D)

E)

Unlock Deck
Unlock for access to all 150 flashcards in this deck.
Unlock Deck
k this deck
71
Find the exact value of the given expression. 
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

Unlock Deck
Unlock for access to all 150 flashcards in this deck.
Unlock Deck
k this deck
72
Find the exact solutions of the given equation in the interval
. 
A)
B)
C)
D)
E)


A)

B)

C)

D)

E)

Unlock Deck
Unlock for access to all 150 flashcards in this deck.
Unlock Deck
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73
Find the exact value of the given expression using a sum or difference formula. 
A)
B)
C)
D)

A)

B)

C)

D)

Unlock Deck
Unlock for access to all 150 flashcards in this deck.
Unlock Deck
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74
Write the given expression as an algebraic expression. 
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

Unlock Deck
Unlock for access to all 150 flashcards in this deck.
Unlock Deck
k this deck
75
Write the given expression as the sine of an angle. 
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

Unlock Deck
Unlock for access to all 150 flashcards in this deck.
Unlock Deck
k this deck
76
Use the half-angle formulas to determine the exact value of the given trigonometric expression. 
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

Unlock Deck
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Unlock Deck
k this deck
77
Find the exact value of the given expression. 
A)
B)
C)
D)

A)

B)

C)

D)

Unlock Deck
Unlock for access to all 150 flashcards in this deck.
Unlock Deck
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78
If
, use trigonometric substitution to write
as a trigonometric function of , where
.
A)
B)
C)
D)
E)



A)

B)

C)

D)

E)

Unlock Deck
Unlock for access to all 150 flashcards in this deck.
Unlock Deck
k this deck
79
Use the product-to-sum formula to write the given product as a sum or difference. 
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

Unlock Deck
Unlock for access to all 150 flashcards in this deck.
Unlock Deck
k this deck
80
If
, use trigonometric substitution to write
as a trigonometric function of , where
.
A)
B)
C)
D)
E)



A)

B)

C)

D)

E)

Unlock Deck
Unlock for access to all 150 flashcards in this deck.
Unlock Deck
k this deck