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Deck 34: Sum and Difference Formulas
Full screen (f)
Question
A weight is attached to a spring suspended vertically from a ceiling.When a driving force is applied to the system,the weight moves vertically from its equilibrium position,and this motion is modeled by 
where y is the distance from equilibrium (in feet)and t is the time (in seconds).
Use the identity
where 
,to write the model in the form 
.
A)
B)
C)
D)
E)
where y is the distance from equilibrium (in feet)and t is the time (in seconds).
Use the identity
where ,to write the model in the form .
A)
B)
C)
D)
E)
Question
Find the expression as the sine of an angle. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find the expression as the sine or cosine of an angle. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Simplify the expression algebraically. 
A)
B)0
C)
D)1
E)6
A)
B)0
C)
D)1
E)6
Question
Simplify the expression algebraically. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find the expression as the tangent of an angle. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Simplify the expression algebraically. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Simplify the expression algebraically. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Simplify the expression algebraically. 
A)-
B)
C)
D)
E)
A)-
B)
C)
D)
E)
Question
Find the expression as the sine or cosine of an angle. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find the expression as the tangent of an angle. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Simplify the expression algebraically. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Simplify the expression algebraically. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
A weight is attached to a spring suspended vertically from a ceiling.When a driving force is applied to the system,the weight moves vertically from its equilibrium position,and this motion is modeled by 
where y is the distance from equilibrium (in feet)and t is the time (in seconds). Find the amplitude of the oscillations of the weight.
A)
B)
C)
D)
E)
where y is the distance from equilibrium (in feet)and t is the time (in seconds). Find the amplitude of the oscillations of the weight.
A)
B)
C)
D)
E)
Question
Find the expression as the tangent of an angle. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Simplify the expression algebraically. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Simplify the expression algebraically. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find the expression as the cosine of an angle. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Simplify the expression algebraically. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find the expression as the sine of an angle. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Use the formula 
,where 
to rewrite the trigonometric expression in the following form. 
A)
B)9
C)9
D)
E)2
,where to rewrite the trigonometric expression in the following form. A)
B)9
C)9
D)
E)2
Question
Simplify the following expression algebraically. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Use the formula 
,where 
,to rewrite the trigonometric expression in the following form. 
A)
B)
C)
D)
E)
,where ,to rewrite the trigonometric expression in the following form. A)
B)
C)
D)
E)
Question
Simplify the following expression algebraically. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Use the formula 
,where 
,to rewrite the trigonometric expression in the following form. 
A)
B)
C)
D)
E)
,where ,to rewrite the trigonometric expression in the following form. A)
B)
C)
D)
E)
Question
Simplify the following expression algebraically. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Use a graphing utility to select correct graph of 
and 
in the same viewing window.Use the graphs to determine whether 
.Explain your reasoning. 
A)
No, 
because their graphs are different.
B)
Yes, 
because their graphs are different.
C)
Yes, 
because their graphs are same.
D)
No, 
because their graphs are Same.
E)
No, 
because their graphs are different.
and in the same viewing window.Use the graphs to determine whether .Explain your reasoning. A)
No, because their graphs are different.B)
Yes, because their graphs are different.C)
Yes, because their graphs are same.D)
No, because their graphs are Same.E)
No, because their graphs are different. Question
Use the formula 
,where 
to rewrite the trigonometric expression in the following form. 
A)
B)
C)3
D)
E)
,where to rewrite the trigonometric expression in the following form. A)
B)
C)3
D)
E)
Question
Simplify the following expression algebraically. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Use a graphing utility to select the correct graph of 
and 
in the same viewing window.Use the graphs to determine whether 
.Explain your reasoning. 
A)
No, 
because their graphs are different.
B)
No, 
because their graphs are Same.
C)
Yes, 
because their graphs are different.
D)
Yes, 
because their graphs are same.
E)
No, 
because their graphs are different.
and in the same viewing window.Use the graphs to determine whether .Explain your reasoning. A)
No, because their graphs are different.B)
No, because their graphs are Same.C)
Yes, because their graphs are different.D)
Yes, because their graphs are same.E)
No, because their graphs are different. Question
Use the formula 
,where 
to rewrite the trigonometric expression in the following form. 
A)6
B)
C)
D)13
E)13
,where to rewrite the trigonometric expression in the following form. A)6
B)
C)
D)13
E)13
Question
Use the formula 
,where 
,to rewrite the trigonometric expression in the form. 
A)
B)
C)
D)
E)
,where ,to rewrite the trigonometric expression in the form. A)
B)
C)
D)
E)
Question
Use the formula 
,where 
,to rewrite the trigonometric expression in the form 
9 
A)
B)
C)
D)
E)
,where ,to rewrite the trigonometric expression in the form 9 A)
B)
C)
D)
E)
Question
Find the exact value of the given expression using a sum or difference formula. 
A)
B)
C)
D)
A)
B)
C)
D)
Question
Find the exact value of the given expression. 
A)
B)
C)
D)
A)
B)
C)
D)
Question
Use the formula 
,where 
,to rewrite the trigonometric expression in the following form. 
A)2
B)
C)
D)2
E)8
,where ,to rewrite the trigonometric expression in the following form. A)2
B)
C)
D)2
E)8
Question
Find the exact value of the given expression. 
A)
B)
C)
D)
A)
B)
C)
D)
Question
Use the formula 
,where 
to rewrite the trigonometric expression in the following form. 
A)
B)
C)7
D)3
E)3
,where to rewrite the trigonometric expression in the following form. A)
B)
C)7
D)3
E)3
Question
Use the formula 
,where 
,to rewrite the trigonometric expression in the following form. 
A)
B)
C)
D)
E)
,where ,to rewrite the trigonometric expression in the following form. A)
B)
C)
D)
E)
Question
Find the exact value of the given expression using a sum or difference formula. 
A)
B)
C)
D)
A)
B)
C)
D)
Question
Find the exact value of 
given that 
and 
.(Both u and v are in Quadrant II. )
A)
B)
C)
D)
E)
given that and .(Both u and v are in Quadrant II. )A)
B)
C)
D)
E)
Question
Find the exact value of the given expression. 
A)
B)
C)
D)
A)
B)
C)
D)
Question
Simplify the given expression algebraically. 
A)
B)
C)
D)1
E)
A)
B)
C)
D)1
E)
Question
Write the given expression as the cosine of an angle. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find the exact value of the given expression. 
A)
B)
C)
D)
A)
B)
C)
D)
Question
Write the given expression as the tangent of an angle. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find the exact solutions of the given equation in the interval [0,2π). sin 2x = sin x
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Simplify the given expression algebraically. 
A)
B)
C)
D)
E)1
A)
B)
C)
D)
E)1
Question
Write the given expression as the cosine of an angle. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Write the given expression as the sine of an angle. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Write the given expression as an algebraic expression. cos(arccos x - arcsin x)
A)
B)
C)
D)1
E)
A)
B)
C)
D)1
E)
Question
Find the exact value of 
given that 
and 
.(Both u and v are in Quadrant II. )
A)
B)
C)
D)
E)
given that and .(Both u and v are in Quadrant II. )A)
B)
C)
D)
E)
Question
Find the exact value of the given expression. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find the exact value of 
given that 
and 
.(Both u and v are in Quadrant II. )
A)
B)
C)
D)
E)
given that and .(Both u and v are in Quadrant II. )A)
B)
C)
D)
E)
Question
Write the given expression as the tangent of an angle. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find the exact value of the given expression using a sum or difference formula. 
A)
B)
C)
D)
A)
B)
C)
D)
Question
Write the given expression as the sine of an angle. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Evaluate the expression. 
A)
B)0
C)
D)
E)
A)
B)0
C)
D)
E)
Question
Find the exact value of 
given that 
and 
.(Both u and v are in Quadrant II. )
A)
B)
C)
D)
E)
given that and .(Both u and v are in Quadrant II. )A)
B)
C)
D)
E)
Question
Find the exact value of the given expression using a sum or difference formula. 
A)
B)
C)
D)
A)
B)
C)
D)
Question
Find the exact solutions of the given equation in the interval 
. sin 4x= -2sin 2x
A)
B)
C)
D)
E)
. sin 4x= -2sin 2xA)
B)
C)
D)
E)
Question
Verify the given identity. 
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Deck 34: Sum and Difference Formulas
1
A weight is attached to a spring suspended vertically from a ceiling.When a driving force is applied to the system,the weight moves vertically from its equilibrium position,and this motion is modeled by where y is the distance from equilibrium (in feet)and t is the time (in seconds).
Use the identity where ,to write the model in the form .
A)
B)
C)
D)
E)
where y is the distance from equilibrium (in feet)and t is the time (in seconds).
Use the identity
where ,to write the model in the form .
A)
B)
C)
D)
E)
2
Find the expression as the sine of an angle.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
3
Find the expression as the sine or cosine of an angle.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
4
Simplify the expression algebraically.
A)
B)0
C)
D)1
E)6
A)
B)0
C)
D)1
E)6
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5
Simplify the expression algebraically.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 62 flashcards in this deck.
Unlock Deck
k this deck
6
Find the expression as the tangent of an angle.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 62 flashcards in this deck.
Unlock Deck
k this deck
7
Simplify the expression algebraically.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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Unlock Deck
k this deck
8
Simplify the expression algebraically.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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Unlock Deck
k this deck
9
Simplify the expression algebraically.
A)-
B)
C)
D)
E)
A)-
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 62 flashcards in this deck.
Unlock Deck
k this deck
10
Find the expression as the sine or cosine of an angle.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 62 flashcards in this deck.
Unlock Deck
k this deck
11
Find the expression as the tangent of an angle.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 62 flashcards in this deck.
Unlock Deck
k this deck
12
Simplify the expression algebraically.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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Unlock for access to all 62 flashcards in this deck.
Unlock Deck
k this deck
13
Simplify the expression algebraically.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 62 flashcards in this deck.
Unlock Deck
k this deck
14
A weight is attached to a spring suspended vertically from a ceiling.When a driving force is applied to the system,the weight moves vertically from its equilibrium position,and this motion is modeled by where y is the distance from equilibrium (in feet)and t is the time (in seconds). Find the amplitude of the oscillations of the weight.
A)
B)
C)
D)
E)
where y is the distance from equilibrium (in feet)and t is the time (in seconds). Find the amplitude of the oscillations of the weight.
A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 62 flashcards in this deck.
Unlock Deck
k this deck
15
Find the expression as the tangent of an angle.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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Unlock Deck
k this deck
16
Simplify the expression algebraically.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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Unlock Deck
k this deck
17
Simplify the expression algebraically.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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Unlock for access to all 62 flashcards in this deck.
Unlock Deck
k this deck
18
Find the expression as the cosine of an angle.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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Unlock for access to all 62 flashcards in this deck.
Unlock Deck
k this deck
19
Simplify the expression algebraically.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 62 flashcards in this deck.
Unlock Deck
k this deck
20
Find the expression as the sine of an angle.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 62 flashcards in this deck.
Unlock Deck
k this deck
21
Use the formula ,where to rewrite the trigonometric expression in the following form.
A)
B)9
C)9
D)
E)2
,where to rewrite the trigonometric expression in the following form. A)
B)9
C)9
D)
E)2
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Unlock for access to all 62 flashcards in this deck.
Unlock Deck
k this deck
22
Simplify the following expression algebraically.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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Unlock Deck
k this deck
23
Use the formula ,where ,to rewrite the trigonometric expression in the following form.
A)
B)
C)
D)
E)
,where ,to rewrite the trigonometric expression in the following form. A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 62 flashcards in this deck.
Unlock Deck
k this deck
24
Simplify the following expression algebraically.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 62 flashcards in this deck.
Unlock Deck
k this deck
25
Use the formula ,where ,to rewrite the trigonometric expression in the following form.
A)
B)
C)
D)
E)
,where ,to rewrite the trigonometric expression in the following form. A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 62 flashcards in this deck.
Unlock Deck
k this deck
26
Simplify the following expression algebraically.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 62 flashcards in this deck.
Unlock Deck
k this deck
27
Use a graphing utility to select correct graph of and in the same viewing window.Use the graphs to determine whether .Explain your reasoning.
A) No, because their graphs are different.
B) Yes, because their graphs are different.
C) Yes, because their graphs are same.
D) No, because their graphs are Same.
E) No, because their graphs are different.
and in the same viewing window.Use the graphs to determine whether .Explain your reasoning. A)
No, because their graphs are different.B)
Yes, because their graphs are different.C)
Yes, because their graphs are same.D)
No, because their graphs are Same.E)
No, because their graphs are different. Unlock Deck
Unlock for access to all 62 flashcards in this deck.
Unlock Deck
k this deck
28
Use the formula ,where to rewrite the trigonometric expression in the following form.
A)
B)
C)3
D)
E)
,where to rewrite the trigonometric expression in the following form. A)
B)
C)3
D)
E)
Unlock Deck
Unlock for access to all 62 flashcards in this deck.
Unlock Deck
k this deck
29
Simplify the following expression algebraically.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 62 flashcards in this deck.
Unlock Deck
k this deck
30
Use a graphing utility to select the correct graph of and in the same viewing window.Use the graphs to determine whether .Explain your reasoning.
A) No, because their graphs are different.
B) No, because their graphs are Same.
C) Yes, because their graphs are different.
D) Yes, because their graphs are same.
E) No, because their graphs are different.
and in the same viewing window.Use the graphs to determine whether .Explain your reasoning. A)
No, because their graphs are different.B)
No, because their graphs are Same.C)
Yes, because their graphs are different.D)
Yes, because their graphs are same.E)
No, because their graphs are different. Unlock Deck
Unlock for access to all 62 flashcards in this deck.
Unlock Deck
k this deck
31
Use the formula ,where to rewrite the trigonometric expression in the following form.
A)6
B)
C)
D)13
E)13
,where to rewrite the trigonometric expression in the following form. A)6
B)
C)
D)13
E)13
Unlock Deck
Unlock for access to all 62 flashcards in this deck.
Unlock Deck
k this deck
32
Use the formula ,where ,to rewrite the trigonometric expression in the form.
A)
B)
C)
D)
E)
,where ,to rewrite the trigonometric expression in the form. A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 62 flashcards in this deck.
Unlock Deck
k this deck
33
Use the formula ,where ,to rewrite the trigonometric expression in the form 9
A)
B)
C)
D)
E)
,where ,to rewrite the trigonometric expression in the form 9 A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 62 flashcards in this deck.
Unlock Deck
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34
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 62 flashcards in this deck.
Unlock Deck
k this deck
35
Find the exact value of the given expression.
A)
B)
C)
D)
A)
B)
C)
D)
Unlock Deck
Unlock for access to all 62 flashcards in this deck.
Unlock Deck
k this deck
36
Use the formula ,where ,to rewrite the trigonometric expression in the following form.
A)2
B)
C)
D)2
E)8
,where ,to rewrite the trigonometric expression in the following form. A)2
B)
C)
D)2
E)8
Unlock Deck
Unlock for access to all 62 flashcards in this deck.
Unlock Deck
k this deck
37
Find the exact value of the given expression.
A)
B)
C)
D)
A)
B)
C)
D)
Unlock Deck
Unlock for access to all 62 flashcards in this deck.
Unlock Deck
k this deck
38
Use the formula ,where to rewrite the trigonometric expression in the following form.
A)
B)
C)7
D)3
E)3
,where to rewrite the trigonometric expression in the following form. A)
B)
C)7
D)3
E)3
Unlock Deck
Unlock for access to all 62 flashcards in this deck.
Unlock Deck
k this deck
39
Use the formula ,where ,to rewrite the trigonometric expression in the following form.
A)
B)
C)
D)
E)
,where ,to rewrite the trigonometric expression in the following form. A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 62 flashcards in this deck.
Unlock Deck
k this deck
40
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 62 flashcards in this deck.
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41
Find the exact value of given that and .(Both u and v are in Quadrant II. )
A)
B)
C)
D)
E)
given that and .(Both u and v are in Quadrant II. )A)
B)
C)
D)
E)
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42
Find the exact value of the given expression.
A)
B)
C)
D)
A)
B)
C)
D)
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43
Simplify the given expression algebraically.
A)
B)
C)
D)1
E)
A)
B)
C)
D)1
E)
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44
Write the given expression as the cosine of an angle.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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45
Find the exact value of the given expression.
A)
B)
C)
D)
A)
B)
C)
D)
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46
Write the given expression as the tangent of an angle.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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47
Find the exact solutions of the given equation in the interval [0,2π). sin 2x = sin x
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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48
Simplify the given expression algebraically.
A)
B)
C)
D)
E)1
A)
B)
C)
D)
E)1
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49
Write the given expression as the cosine of an angle.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
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Unlock Deck
k this deck
50
Write the given expression as the sine of an angle.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
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Unlock Deck
k this deck
51
Write the given expression as an algebraic expression. cos(arccos x - arcsin x)
A)
B)
C)
D)1
E)
A)
B)
C)
D)1
E)
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Unlock Deck
k this deck
52
Find the exact value of given that and .(Both u and v are in Quadrant II. )
A)
B)
C)
D)
E)
given that and .(Both u and v are in Quadrant II. )A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 62 flashcards in this deck.
Unlock Deck
k this deck
53
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 62 flashcards in this deck.
Unlock Deck
k this deck
54
Find the exact value of given that and .(Both u and v are in Quadrant II. )
A)
B)
C)
D)
E)
given that and .(Both u and v are in Quadrant II. )A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 62 flashcards in this deck.
Unlock Deck
k this deck
55
Write the given expression as the tangent of an angle.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 62 flashcards in this deck.
Unlock Deck
k this deck
56
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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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 62 flashcards in this deck.
Unlock Deck
k this deck
58
Evaluate the expression.
A)
B)0
C)
D)
E)
A)
B)0
C)
D)
E)
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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)
given that and .(Both u and v are in Quadrant II. )A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 62 flashcards in this deck.
Unlock Deck
k this deck
60
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 62 flashcards in this deck.
Unlock Deck
k this deck
61
Find the exact solutions of the given equation in the interval . sin 4x= -2sin 2x
A)
B)
C)
D)
E)
. sin 4x= -2sin 2xA)
B)
C)
D)
E)
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Unlock Deck
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62
Verify the given identity.
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Unlock Deck
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