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Deck 35: Multiple Angle and Product to Sum Formulas
Full screen (f)
Question
Use the product-to-sum formulas to rewrite the product as a sum or difference. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Use the sum-to-product formulas to rewrite the sum or difference as a product. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Use the product-to-sum formulas to rewrite the product as a sum or difference. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Use the product-to-sum formulas to rewrite the product as a sum or difference. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Question
Use the sum-to-product formulas to rewrite the sum or difference as a product. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Use the product-to-sum formulas to rewrite the product as a sum or difference. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Question
Use the figure to find the exact value of the trigonometric function.
Csc 2θ
A = 1,b = 6
A)
B)
C)
D)
E)
Csc 2θ
A = 1,b = 6
A)
B)
C)
D)
E)
Question
Use the half-angle formulas to simplify the expression. 
A)|sin 5x|
B)- |sin x|
C)|sin 10x|
D)- |sin 5x|
E)|sin x|
A)|sin 5x|
B)- |sin x|
C)|sin 10x|
D)- |sin 5x|
E)|sin x|
Question
Use the figure to find the exact value of the trigonometric function.
Cot 2θ
A = 1,b = 6
A)
B)
C)
D)
E)
Cot 2θ
A = 1,b = 6
A)
B)
C)
D)
E)
Question
Use the figure to find the exact value of the trigonometric function.
Tan 2θ
A = 1,b = 6
A)
B)
C)
D)
E)
Tan 2θ
A = 1,b = 6
A)
B)
C)
D)
E)
Question
Use the half-angle formulas to simplify the expression. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Use the figure to find the exact value of the trigonometric function.
Cos 2θ
A = 1,b = 2
A)
B)
C)
D)
E)
Cos 2θ
A = 1,b = 2
A)
B)
C)
D)
E)
Question
Use a double-angle formula to rewrite the expression. 
A)sin x
B)2 sin x
C)2 sin 2x
D) sin x
E) sin 2x
A)sin x
B)2 sin x
C)2 sin 2x
D) sin x
E) sin 2x
Question
Use the figure to find the exact value of the trigonometric function.
Sec 2θ
A = 1,b = 8
A)
B)
C)
D)
E)
Sec 2θ
A = 1,b = 8
A)
B)
C)
D)
E)
Question
Use the half-angle formulas to simplify the expression. 
A)- |cos x|
B)|cos x|
C)|cos 4x|
D)- |cos 4x|
E)- |cos 8x|
A)- |cos x|
B)|cos x|
C)|cos 4x|
D)- |cos 4x|
E)- |cos 8x|
Question
Use the half-angle formulas to simplify the expression. 
A)- |cot x|
B)- |3 tan x|
C)- |3 tan 6x|
D)- |3 cot 3x|
E)- |cot 3x|
A)- |cot x|
B)- |3 tan x|
C)- |3 tan 6x|
D)- |3 cot 3x|
E)- |cot 3x|
Question
Question
Use the figure to find the exact value of the trigonometric function.
Sin 2θ
A = 1,b = 2
A)
B)
C)
D)
E)
Sin 2θ
A = 1,b = 2
A)
B)
C)
D)
E)
Question
Use the figure below to determine the exact value of the given function. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Use a double angle formula to rewrite the given expression. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Convert the expression. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find the exact solutions of the given equation in the interval [0,2π). 
A)
B)
C)
D)x = 0
E)
A)
B)
C)
D)x = 0
E)
Question
Convert the expression. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
The mach number M of an airplane is the ratio of its speed to the speed of sound.When an airplane travels faster than the speed of sound,the sound waves form a cone behind the airplane (see figure).The mach number is related to the apex angle θ of the cone by 
. 
Rewrite the equation in terms of θ.
A)
B)
C)
D)
E)
. Rewrite the equation in terms of θ.
A)
B)
C)
D)
E)
Question
Use the sum-to-product formulas to rewrite the sum or difference as a product.
Cos 3θ + cos 8θ
A)
B)
C)
D)
E)
Cos 3θ + cos 8θ
A)
B)
C)
D)
E)
Question
Use the figure to find the exact value of the trigonometric function. 
sin 2α
A)
B)
C)
D)
E)
sin 2α
A)
B)
C)
D)
E)
Question
Convert the expression. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Convert the expression. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Convert the expression. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Use the sum-to-product formulas to rewrite the sum or difference as a product. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Convert the expression. 
A)2 cos b
B)cos 2b
C)cos b
D)2 cos 2b
E)4 cos b
A)2 cos b
B)cos 2b
C)cos b
D)2 cos 2b
E)4 cos b
Question
When two railroad tracks merge,the overlapping portions of the tracks are in the shapes of circular arcs (see figure).The radius of each arc r (in feet)and the angle θ are related by 
Write a formula for x in terms of cos θ. 
A)
B)
C)
D)
E)
Write a formula for x in terms of cos θ. A)
B)
C)
D)
E)
Question
Convert the expression. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Use a double-angle formula to find the exact value of cos2u when 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Use the figure to find the exact value of the trigonometric function. 
cos 2β
A)
B)
C)
D)
E)
cos 2β
A)
B)
C)
D)
E)
Question
Convert the expression. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find the exact solutions of the given equation in the interval [0,2π). 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Use the sum-to-product formulas to select the sum or difference as a product. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
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)
Question
Use the figure below to find the exact value of the given trigonometric expression. 
10 24
(figure not necessarily to scale)
A)
B)
C)
D)
E)
10 24(figure not necessarily to scale)
A)
B)
C)
D)
E)
Question
Use the half-angle formula to simplify the given expression. 
A)cos |2x|
B)cos |8x|
C)cos |16x|
D)cos |32x|
E)cos |4x|
A)cos |2x|
B)cos |8x|
C)cos |16x|
D)cos |32x|
E)cos |4x|
Question
Use the figure below to find the exact value of the given trigonometric expression. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
The range of a projectile fired at an angle θ with the horizontal and with an initial velocity of v0 feet per second is 
where r is measured in feet.A golfer strikes a golf ball at 90 feet per second.Ignoring the effects of air resistance,at what angle must the golfer hit the ball so that it travels 150 feet? (Round your answer to the nearest degree. )
A)14°
B)36°
C)18°
D)27°
E)41°
where r is measured in feet.A golfer strikes a golf ball at 90 feet per second.Ignoring the effects of air resistance,at what angle must the golfer hit the ball so that it travels 150 feet? (Round your answer to the nearest degree. )A)14°
B)36°
C)18°
D)27°
E)41°
Question
Find all solutions of the given equation in the interval [0,2π). 
A)
B)
C)
D)
E)x = 0
A)
B)
C)
D)
E)x = 0
Question
Find all solutions of the given equation in the interval [0,2π). 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
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)
Question
Use the sum-to-product formulas to find the exact value of the given expression. 
A)
B)1
C)
D)-1
E)0
A)
B)1
C)
D)-1
E)0
Question
Use the sum-to-product formulas to write the given expression as a product. 
A)2 sin 4θ cos θ
B)-2 sin 4θ sin θ
C)-2 cos 4θ cos θ
D)2 cos 4θ sin θ
E)2 cos 4θ cos θ
A)2 sin 4θ cos θ
B)-2 sin 4θ sin θ
C)-2 cos 4θ cos θ
D)2 cos 4θ sin θ
E)2 cos 4θ cos θ
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Deck 35: Multiple Angle and Product to Sum Formulas
1
Use the product-to-sum formulas to rewrite the product as a sum or difference.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
2
Use the sum-to-product formulas to rewrite the sum or difference as a product.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
3
Use the product-to-sum formulas to rewrite the product as a sum or difference.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
4
Use the product-to-sum formulas to rewrite the product as a sum or difference.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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5
Use a double-angle formula to rewrite the expression.
10 cos2 x - 5
A)5 cos x
B)cos 5x
C)10 cos 2x
D)10 cos x
E)5 cos 2x
10 cos2 x - 5
A)5 cos x
B)cos 5x
C)10 cos 2x
D)10 cos x
E)5 cos 2x
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6
Use the sum-to-product formulas to rewrite the sum or difference as a product.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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Unlock for access to all 50 flashcards in this deck.
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7
Use the product-to-sum formulas to rewrite the product as a sum or difference.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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Unlock Deck
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8
Use a double-angle formula to rewrite the expression.
3 - 6 sin2 x
A)6 cos x
B)3 sin 2x
C)3 sin x
D)3 cos 2x
E)6 cos 2x
3 - 6 sin2 x
A)6 cos x
B)3 sin 2x
C)3 sin x
D)3 cos 2x
E)6 cos 2x
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9
Use the figure to find the exact value of the trigonometric function.
Csc 2θ
A = 1,b = 6
A)
B)
C)
D)
E)
Csc 2θ
A = 1,b = 6
A)
B)
C)
D)
E)
Unlock Deck
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Unlock Deck
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10
Use the half-angle formulas to simplify the expression.
A)|sin 5x|
B)- |sin x|
C)|sin 10x|
D)- |sin 5x|
E)|sin x|
A)|sin 5x|
B)- |sin x|
C)|sin 10x|
D)- |sin 5x|
E)|sin x|
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11
Use the figure to find the exact value of the trigonometric function.
Cot 2θ
A = 1,b = 6
A)
B)
C)
D)
E)
Cot 2θ
A = 1,b = 6
A)
B)
C)
D)
E)
Unlock Deck
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Unlock Deck
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12
Use the figure to find the exact value of the trigonometric function.
Tan 2θ
A = 1,b = 6
A)
B)
C)
D)
E)
Tan 2θ
A = 1,b = 6
A)
B)
C)
D)
E)
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13
Use the half-angle formulas to simplify the expression.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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Unlock Deck
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14
Use the figure to find the exact value of the trigonometric function.
Cos 2θ
A = 1,b = 2
A)
B)
C)
D)
E)
Cos 2θ
A = 1,b = 2
A)
B)
C)
D)
E)
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15
Use a double-angle formula to rewrite the expression.
A)sin x
B)2 sin x
C)2 sin 2x
D) sin x
E) sin 2x
A)sin x
B)2 sin x
C)2 sin 2x
D) sin x
E) sin 2x
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16
Use the figure to find the exact value of the trigonometric function.
Sec 2θ
A = 1,b = 8
A)
B)
C)
D)
E)
Sec 2θ
A = 1,b = 8
A)
B)
C)
D)
E)
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17
Use the half-angle formulas to simplify the expression.
A)- |cos x|
B)|cos x|
C)|cos 4x|
D)- |cos 4x|
E)- |cos 8x|
A)- |cos x|
B)|cos x|
C)|cos 4x|
D)- |cos 4x|
E)- |cos 8x|
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18
Use the half-angle formulas to simplify the expression.
A)- |cot x|
B)- |3 tan x|
C)- |3 tan 6x|
D)- |3 cot 3x|
E)- |cot 3x|
A)- |cot x|
B)- |3 tan x|
C)- |3 tan 6x|
D)- |3 cot 3x|
E)- |cot 3x|
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19
Use a double-angle formula to rewrite the expression.
2 sin2 x - 1
A)cos x
B)cos 2x
C)-2 cos x
D)2 cos 2x
E)- cos 2x
2 sin2 x - 1
A)cos x
B)cos 2x
C)-2 cos x
D)2 cos 2x
E)- cos 2x
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20
Use the figure to find the exact value of the trigonometric function.
Sin 2θ
A = 1,b = 2
A)
B)
C)
D)
E)
Sin 2θ
A = 1,b = 2
A)
B)
C)
D)
E)
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Unlock Deck
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21
Use the figure below to determine the exact value of the given function.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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22
Use a double angle formula to rewrite the given expression.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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Unlock Deck
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23
Convert the expression.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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Unlock Deck
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24
Find the exact solutions of the given equation in the interval [0,2π).
A)
B)
C)
D)x = 0
E)
A)
B)
C)
D)x = 0
E)
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25
Convert the expression.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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26
The mach number M of an airplane is the ratio of its speed to the speed of sound.When an airplane travels faster than the speed of sound,the sound waves form a cone behind the airplane (see figure).The mach number is related to the apex angle θ of the cone by . Rewrite the equation in terms of θ.
A)
B)
C)
D)
E)
. Rewrite the equation in terms of θ.
A)
B)
C)
D)
E)
Unlock Deck
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27
Use the sum-to-product formulas to rewrite the sum or difference as a product.
Cos 3θ + cos 8θ
A)
B)
C)
D)
E)
Cos 3θ + cos 8θ
A)
B)
C)
D)
E)
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28
Use the figure to find the exact value of the trigonometric function. sin 2α
A)
B)
C)
D)
E)
sin 2α
A)
B)
C)
D)
E)
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29
Convert the expression.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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Unlock Deck
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30
Convert the expression.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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Unlock Deck
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31
Convert the expression.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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Unlock Deck
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32
Use the sum-to-product formulas to rewrite the sum or difference as a product.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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Unlock Deck
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33
Convert the expression.
A)2 cos b
B)cos 2b
C)cos b
D)2 cos 2b
E)4 cos b
A)2 cos b
B)cos 2b
C)cos b
D)2 cos 2b
E)4 cos b
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34
When two railroad tracks merge,the overlapping portions of the tracks are in the shapes of circular arcs (see figure).The radius of each arc r (in feet)and the angle θ are related by Write a formula for x in terms of cos θ.
A)
B)
C)
D)
E)
Write a formula for x in terms of cos θ. A)
B)
C)
D)
E)
Unlock Deck
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Unlock Deck
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35
Convert the expression.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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Unlock Deck
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36
Use a double-angle formula to find the exact value of cos2u when
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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37
Use the figure to find the exact value of the trigonometric function. cos 2β
A)
B)
C)
D)
E)
cos 2β
A)
B)
C)
D)
E)
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Unlock Deck
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38
Convert the expression.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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Unlock for access to all 50 flashcards in this deck.
Unlock Deck
k this deck
39
Find the exact solutions of the given equation in the interval [0,2π).
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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Unlock Deck
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40
Use the sum-to-product formulas to select the sum or difference as a product.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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Unlock Deck
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41
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
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42
Use the figure below to find the exact value of the given trigonometric expression. 10 24
(figure not necessarily to scale)
A)
B)
C)
D)
E)
10 24(figure not necessarily to scale)
A)
B)
C)
D)
E)
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Unlock Deck
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43
Use the half-angle formula to simplify the given expression.
A)cos |2x|
B)cos |8x|
C)cos |16x|
D)cos |32x|
E)cos |4x|
A)cos |2x|
B)cos |8x|
C)cos |16x|
D)cos |32x|
E)cos |4x|
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44
Use the figure below to find 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
45
The range of a projectile fired at an angle θ with the horizontal and with an initial velocity of v0 feet per second is where r is measured in feet.A golfer strikes a golf ball at 90 feet per second.Ignoring the effects of air resistance,at what angle must the golfer hit the ball so that it travels 150 feet? (Round your answer to the nearest degree. )
A)14°
B)36°
C)18°
D)27°
E)41°
where r is measured in feet.A golfer strikes a golf ball at 90 feet per second.Ignoring the effects of air resistance,at what angle must the golfer hit the ball so that it travels 150 feet? (Round your answer to the nearest degree. )A)14°
B)36°
C)18°
D)27°
E)41°
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46
Find all solutions of the given equation in the interval [0,2π).
A)
B)
C)
D)
E)x = 0
A)
B)
C)
D)
E)x = 0
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47
Find all solutions of the given equation in the interval [0,2π).
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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k this deck
48
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)
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49
Use the sum-to-product formulas to find the exact value of the given expression.
A)
B)1
C)
D)-1
E)0
A)
B)1
C)
D)-1
E)0
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50
Use the sum-to-product formulas to write the given expression as a product.
A)2 sin 4θ cos θ
B)-2 sin 4θ sin θ
C)-2 cos 4θ cos θ
D)2 cos 4θ sin θ
E)2 cos 4θ cos θ
A)2 sin 4θ cos θ
B)-2 sin 4θ sin θ
C)-2 cos 4θ cos θ
D)2 cos 4θ sin θ
E)2 cos 4θ cos θ
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k this deck
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