Deck 6: Analytic Trigonometry
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Deck 6: Analytic Trigonometry
1
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)


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

A)

B)

C)

D)


3
Find the exact solutions of the given equation in the interval
. 
A)
B)
C)
D)
E)


A)

B)

C)

D)

E)


4
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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5
Write the given expression as an algebraic expression. 
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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6
Which of the following is equivalent to the given expression? 
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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7
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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8
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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9
Rewrite
as a single logarithm and then simplify the result.
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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10
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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Unlock Deck
k this deck
11
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
12
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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13
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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14
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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15
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
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16
Write the given expression as the sine of an angle. 
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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17
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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18
Write the given expression as the cosine of an angle. 
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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Unlock Deck
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19
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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20
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
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21
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
22
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
23
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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Unlock Deck
k this deck
24
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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Unlock for access to all 150 flashcards in this deck.
Unlock Deck
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25
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
26
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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27
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
28
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)

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Unlock Deck
k this deck
29
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
30
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
31
Which of the following is equivalent to the given expression? 
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

Unlock Deck
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Unlock Deck
k this deck
32
Find the exact value of the given expression. 
A)
B)
C)
D)

A)

B)

C)

D)

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Unlock for access to all 150 flashcards in this deck.
Unlock Deck
k this deck
33
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
Unlock for access to all 150 flashcards in this deck.
Unlock Deck
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34
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
35
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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36
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
37
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
38
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
39
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
40
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
41
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
42
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
43
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
44
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
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
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
47
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
48
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
49
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
50
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
51
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
52
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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53
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
54
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
55
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
56
Which of the following is equivalent to the given expression? 
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

Unlock Deck
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Unlock Deck
k this deck
57
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
58
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
59
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
60
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
61
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
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62
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
63
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
64
Which of the following is equivalent to the given expression? 
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

Unlock Deck
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Unlock Deck
k this deck
65
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
66
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
67
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
68
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
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Unlock Deck
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69
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
70
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
71
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
72
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
73
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
74
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
75
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
76
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
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
k this deck
78
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
79
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
80
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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