chapter 5: analytic trigonometry - crunchy math -...

Chapter 5: Analytic Trigonometry

Page 232 Copyright © Houghton Mifflin Company. All rights reserved.

1. If 1 3sin and cos

2 2x x= = , evaluate the following function.

A)

B)

C)

D)

E)

Ans: B Learning Objective: Evaluate trigonometric function given other trigonometric values Section: 5.1


Copyright © Houghton Mifflin Company. All rights reserved. 33

2. If 4 3csc and cos 0

3x x= < , evaluate the function below.

A)

B)

C)

D)

E)

Ans: C Learning Objective: Evaluate trigonometric function given other trigonometric values Section: 5.1

3. Which of the following is equivalent to the expression below?

A)

B)

C)

D)

E)

Ans: A Learning Objective: Simplify a trigonometric expression Section: 5.1



4. Use fundamental identities to simplify the expression below and then determine which of the following is not equivalent.

A)

B)

C)

D)

E)

Ans: D Learning Objective: Simplify a trigonometric expression Section: 5.1

5. Which of the following is equivalent to the expression below?

A)

B)

C)

D)

E)

Ans: A Learning Objective: Simplify a trigonometric expression Section: 5.1


Copyright © Houghton Mifflin Company. All rights reserved. Page 235

6. Determine which of the following are trigonometric identities.

I. ( ) ( ) ( ) ( )sin cot cos cscθ θ θ θ+ =

II. ( ) ( ) ( )cot sin cos 0θ θ θ− =

III. ( ) ( ) ( ) ( )sin sin cos cscθ θ θ θ+ = A) I is the only identity. D) III is the only identity. B) I and II are the only identities. E) I, II, and III are identities. C) II is the only identity.

Ans: A Learning Objective: Identify trigonometric identities Section: 5.1


I. ( ) ( ) ( )tan sec cscθ θ θ=

II. ( ) ( ) ( )tan csc secθ θ θ=

III. ( ) ( ) ( )csc sec tanθ θ θ=

IV. ( ) ( )tan cos 1θ θ = A) II and IV are the only identities. D) IV is the only identity. B) II is the only identity. E) III is the only identity. C) II, III, and IV are the only identities.

Ans: B Learning Objective: Identify trigonometric identities Section: 5.1



8. Factor; then use fundamental identities to simplify the expression below and determine which of the following is not equivalent.

A)

B)

C)

D)

E)

Ans: C Learning Objective: Apply fundamental identities to determine non-equivalent expression Section: 5.1

9. Factor the expression below and use the fundamental identities to simplify.

( ) ( )4 4cos sinx x−

A) ( ) ( )( ) ( ) ( )( )2 2cos sin cos sinx x x x+ −

B) ( ) ( )( )4cos sinx x−

C) ( ) ( )cos sinx x− D) ( ) ( )( ) ( ) ( )( )cos sin cos sinx x x x+ − E) ( ) ( )( )4 cos sinx x−

Ans: D Learning Objective: Apply fundamental identities to determine equivalent expression Section: 5.1



10. Factor; then use fundamental identities to simplify the expression below and determine which of the following is not equivalent.

A)

B)

C)

D)

E)

Ans: E Learning Objective: Apply fundamental identities to determine non-equivalent expression Section: 5.1

11. Expand the expression below and use fundamental trigonometric identities to simplify.

( ) ( )( )2

sin cosω ω+ A) ( ) ( )2 2sin cosω ω+ D) 1 B) ( )2 tan 1ω + E) ( )2cot 1ω + C) ( ) ( )2sin cos 1ω ω +

Ans: C Learning Objective: Simplify a trigonometric expression Section: 5.1



12. Multiply; then use fundamental identities to simplify the expression below and determine which of the following is not equivalent.

A)

B)

C)

D)

E)

Ans: A Learning Objective: Apply fundamental identities to determine non-equivalent expression Section: 5.1



13. Add or subtract as indicated; then use fundamental identities to simplify the expression below and determine which of the following is not equivalent.

A)

B)

C)

D)

E)

Ans: C Learning Objective: Apply fundamental identities to determine non-equivalent expression Section: 5.1



14. Which of the following is equivalent to the given expression?

A)

B)

C)

D)

E)

Ans: B Learning Objective: Apply fundamental identities to determine equivalent expression Section: 5.1

15.

Rewrite the expression ( )( )

sin1– cos

yy

so that it is not in fractional form.

A) ( ) ( )2sin – sin tany y D) ( ) ( )2sin + sin tany y B) ( ) ( )1– sin tany y E) ( )1– cos y C) ( ) ( )csc + coty y

Ans: C Learning Objective: Rewrite fractional trigonometric expression as non-fraction Section: 5.1



16. Use a graphing utility to determine which of the trigonometric functions is equal to the following expression.

A)

B)

C)



D)

E)

Ans: D Learning Objective: Identify equivalent trigonometric expressions with a graphing utility Section: 5.1

17. If 2 tanx θ= , use trigonometric substitution to write 24 + x as a trigonometric

function of θ , where 02πθ< < .

A) 2sinθ B) 2cosθ C) 2cscθ D) 2secθ E) 2 tanθ Ans: D Learning Objective: Write an algebraic expression as a trigonometric function Section: 5.1

18. Use the trigonometric substitution ( )9secx θ= to write the expression 2 81x − as a

trigonometric function of ,θ where 0 .2πθ< <

A) ( )9 tan θ B) ( )81tan θ C) ( )81sec θ D) ( )9sec θ E) ( )9sec 1θ − Ans: A Learning Objective: Write an algebraic expression as a trigonometric function Section: 5.1



19. If 9 tanx θ= , use trigonometric substitution to write 281 + x as a trigonometric

function of θ , where 2 2π πθ− < < .

A) 9cscθ B) 9secθ C) 9 tanθ D) 9sinθ E) 9cosθ Ans: B Learning Objective: Write an algebraic expression as a trigonometric function Section: 5.1

20. If 2cotx θ= , use trigonometric substitution to write 24 + x as a trigonometric

function of θ , where 0 θ π< < . A) 2cosθ B) 2cscθ C) 2cotθ D) 2secθ E) 2sinθ Ans: B Learning Objective: Write an algebraic expression as a trigonometric function Section: 5.1

21. The rate of change of the function

is given by the expression . Which of the following is its simplification?

A)

B)

C)

D)

E)

Ans: C Learning Objective: Simplify a trigonometric expression Section: 5.1



22. Verify the identity shown below.

Ans:

Learning Objective: Verify a trigonometric identity Section: 5.2


Ans:





Ans:



Ans:





I. ( ) ( )( ) ( )

( ) ( )( ) ( )

cot x + cot y tan x + tan y0

tan x – tan y cot x – cot y+ =

II. ( ) ( )( ) ( )

( ) ( )( ) ( )

cot x cot y tan x tan y1

tan x tan y cot x cot y+ +

+ =+ +

III. ( ) ( )( ) ( ) ( ) ( )cot x tan y

cot y tan xcot x tan y

+= +

A) III is the only identity. D) I and II are the only identities. B) I and III are the only identities. E) I, II, and III are identities. C) II and II are the only identities.

Ans: A Learning Objective: Verify a trigonometric identity Section: 5.2


Ans:





Ans:



Ans:





Ans:




33. Use the cofunction identities to evaluate the expression below without the aid of a calculator. 2 2 2 2sin 34 sin 29 sin 56 sin 61° + ° + ° + °

A) 1 B) 2 C) –1 D) 0 E) 1

2

Ans: B Learning Objective: Evaluate trigonometric expression using cofunction identities Section: 5.2


I. ( ) ( ) ( ) ( )4 4 2 4csc z cot z 1 2cot z 2cot z+ = − +

II. ( ) ( ) ( ) ( )5 3 2 3cot z cot z csc z cot z= −

III. ( ) ( ) ( ) ( )( ) ( )3 2 2 4cot z csc z csc z csc z cot z= − A) I, II, and III are identities. D) II and II are the only identities. B) II is the only identity. E) III is the only identity. C) I is the only identity.

Ans: B Learning Objective: Verify a trigonometric identity Section: 5.2



35. Which of the following is a solution to the given equation?

A)

B)

C)

D)

E)

Ans: D Learning Objective: Verify solution to trigonometric equation Section: 5.3



36. Which of the following is a solution to the given equation?

A)

B)

C)

D)

E)

Ans: D Learning Objective: Verify solution to trigonometric equation Section: 5.3



37. Solve the following equation.

A)

B)

C)

D)

E)

Ans: B Learning Objective: Solve trigonometric equation Section: 5.3


( )2csc 4 0x − =

A) ,

3nπ π+ 2 ,

3nπ π+ where n is an integer

B) 2 ,

3nπ π+ 2 2 ,


C) ,

6nπ π+ 5 ,


D) 2 ,

6nπ π+ 2 2 ,


E) 2 ,

6nπ π+ 5 2 ,


Ans: C Learning Objective: Solve trigonometric equation Section: 5.3




A)

B)

C)

D)

E)



6 Copyright © Houghton Mifflin Company. All rights reserved.


A)

B)

C)

D)

E)


41. Find all solutions of the following equation on the interval [ )0, 2 .π

( )tan + 3 0x =

A) 2 ,3π ,

3π 5 ,

3π 4

3π

D) 5 ,6π 11

6π

B) ,

6π 7

6π

E) ,

3π 4

3π

C) 2 ,3π 5

3π




42. Find all solutions of the following equation on the interval [ )0, 2 .π

( )2csc – 2 0x = A)

,4π 3

4π

D) 5 ,4π 7

4π

B) ,

4π 3 ,

4π 5 ,

4π 7

4π

E) 3 ,4π 5

4π

C) ,

4π 7

4π


43. Find all solutions of the following equation in the interval [ )0, 2π .

A)

B)

C)

D)

E)

Ans: E Learning Objective: Solve trigonometric equation Section: 5.3




A)

B)

C)

D)

E)

Ans: A Learning Objective: Solve trigonometric equation Section: 5.3




A)

B)

C)

D)

E)

Ans: D Learning Objective: Solve trigonometric equation Section: 5.3

46. Approximate the solutions of the equation ( ) ( )22sin + 4sin –1 0x x = by considering its

graph below. Round your answer to one decimal.

A) 0.2, 2.9 B) –1.0, 0.2 C) –1.0, 1.8 D) 0.2, 1.8 E) 1.8, 2.9 Ans: A Learning Objective: Approximate solutions of trigonometric equation with a graph Section: 5.3



47. Approximate the solutions of the equation ( ) ( )22sin 3cos 1x x= + by considering its graph below. Round your answer to one decimal.

A) 2.4, 3.9 B) 2.4, 3.1 C) 3.1, 3.9 D) 1.5, 5.0 E) 1.5, 2.4 Ans: D Learning Objective: Approximate solutions of trigonometric equation with a graph Section: 5.3

48. Approximate the solutions of the equation ( ) ( )csc cot –1x x+ = by considering its graph

below. Round your answer to one decimal.

A) 1.9 B) 1.9, 5.9 C) 4.8 D) 5.9 E) The equation has no solution. Ans: C Learning Objective: Approximate solutions of trigonometric equation with a graph Section: 5.3



49. Solve the multiple-angle equation.

A)

B)

C)

D)

E)

Ans: E Learning Objective: Solve multiple-angle equation Section: 5.3



50. Solve the multiple-angle equation in the interval [ )0, 2π .

A)

B)

C)

D)

E)

Ans: C Learning Objective: Solve multiple-angle equation Section: 5.3

51. Solve the multi-angle equation below.

( ) 3sin 22

x =

A) ,

8nπ π+ ,


B) ,

6nπ π+ ,


C) 2 ,

6nπ π+ 2 ,


D) 2 ,

8nπ π+ 2 ,


E) ,

6nπ π+ ,





52. Solve the multi-angle equation below.

2cos2 2x⎛ ⎞ =⎜ ⎟

⎝ ⎠

A) ,

3nπ π+ 7 ,


B) 2 ,

3nπ π+ 7 2 ,


C) ,

2nπ π+ 7 ,


D) ,

2nπ π+ 7 ,


E) 4 ,

2nπ π+ 7 4 ,



53. Use the graph below to approximate the solutions of the equation

( ) ( )–2cos – sin 0x x = on the interval [ )0, 2 .π Round your answer to one decimal.

A) –2.0, 5.9 B) 2.0, 5.9 C) 5.2, 5.9 D) 2, 5.2 E) –2, 5.2 Ans: D Learning Objective: Approximate solutions of trigonometric equation with a graph Section: 5.3



54. Use a graphing utility to approximate the solutions (to three decimal places) of the given equation in the interval [ )0, 2π .

A)

B)

C)

D)

E)

Ans: E Learning Objective: Approximate solutions to trigonometric equation with graphing utility Section: 5.3

55. Use a graphing utility to approximate the solutions (to three decimal places) of the given

equation in the interval ,2 2π π⎛ ⎞−⎜ ⎟

⎝ ⎠.

A)

B)

C)

D)

E)

Ans: A Learning Objective: Approximate solutions to trigonometric equation with graphing utility Section: 5.3



56. Use the graph of the function ( ) ( ) ( )– cos + sinf x x x= to approximate the maximum

points of the graph in the interval [ ]0, 2 .π Round your answer to one decimal.

A) ( )2.6,1.3 , ( )6.3, –0.8 D) ( )–0.8,6.3 , ( )1.3, 2.6 B) ( )–0.8,6.3 , ( )2.6,1.3 E) ( )1.3, 2.6 , ( )6.3, –0.8 C) ( )2.6, –0.8 , ( )6.3,1.3

Ans: A Learning Objective: Approximate maximum or minimum of a trigonometric function Section: 5.3

57. Solve the following trigonometric equation on the interval [ )0, 2 .π

( ) ( )cos + sin 0x x =

A) 5 ,

4π 7

4π B) 3 ,

4π 7

4π C) ,

4π 7

4π D) ,

4π 5

4π E) 3 ,

4π 5

4π


58. Determine the exact value of the following expression.

( )cos 240 0−

A) 3–

2 B) 1

2 C) 3

2 D) 1–

2 E) 1 3–

2 2

Ans: D Learning Objective: Calculate exact value of expression using sum or difference formula Section: 5.4



59. Find the exact value of the given expression. ( )cos 240 315° + °

A) 1 + 3

2 2 B) 1 – 3

2 2 C) –1 + 3

2 2 D) –1 – 3

2 2


60. Find the exact value of the given expression.

5 7sin3 4π π⎛ ⎞−⎜ ⎟

⎝ ⎠

A) – 3 + 1

2 2 B) 3 + 1

2 2 C) – 3 – 1

2 2 D) 3 – 1

2 2

Ans: A Learning Objective: Calculate exact value of expression using sum or difference formula Section: 5.4

61. Find the exact value of the given expression using a sum or difference formula.

sin 285° A) 3 – 1

2 2 B) 3 + 1

2 2 C) – 3 – 1

2 2 D) – 3 + 1

2 2

Ans: C Learning Objective: Calculate exact value of expression using sum or difference formula Section: 5.4


13cos12

π

A) 3 + 1

2 2 B) – 3 + 1

2 2 C) 3 – 1

2 2 D) – 3 – 1

2 2





7tan12π

A) 1 B) –1 C) 3 + 1

1 – 3 D) 3 – 1

–1 – 3 E) undefined


64. Write the given expression as the cosine of an angle.

cos30 cos55 – sin 30 sin 55° ° ° ° A) ( )cos 55° B) ( )cos 85° C) ( )cos –25° D) ( )cos 30° E) ( )cos –110° Ans: B Learning Objective: Rewrite expression using sum or difference formula Section: 5.4

65. Write the given expression as the sine of an angle.

sin15 cos55 – sin 55 cos15° ° ° ° A) ( )sin –110° B) ( )sin –40° C) ( )sin 70° D) ( )sin 15° E) ( )sin 55° Ans: B Learning Objective: Rewrite expression using sum or difference formula Section: 5.4

66.

Find the exact value of ( )sin u v+ given that 8sin17

u = and 60cos61

v = − . (Both u and v

are in Quadrant II.) A) ( ) 315sin –

1037u v+ =

D) ( ) 812sin –1037

u v+ =

B) ( ) 315sin1037

u v+ = E) ( ) 645sin

1037u v+ =

C) ( ) 645sin –1037

u v+ =




67. Find the exact value of ( )tan u v+ given that 3sin

5u = − and 24cos

25v = . (Both u and v

are in Quadrant IV.) A) ( ) 41tan

75u v+ =

D) ( ) 89tan75

u v+ =

B) ( ) 38tan75

u v+ = E) ( ) 39tan –

25u v+ =

C) ( ) 4tan –3

u v+ =


68.

Find the exact value of ( )cos u v+ given that 7sin25

u = and 12cos13

v = − . (Both u and v

are in Quadrant II.) A) ( ) 12cos

65u v+ =

D) ( ) 246cos –325

u v+ =

B) ( ) 36cos –325

u v+ = E) ( ) 204cos

325u v+ =

C) ( ) 253cos325

u v+ =


69.

Find the exact value of ( )cos u v− given that 8sin17

u = − and 60cos61

v = . (Both u and v

are in Quadrant IV.) A) ( ) 307cos –

1037u v− =

D) ( ) 812cos –1037

u v− =

B) ( ) 980cos –1037

u v− = E) ( ) 988cos

1037u v− =

C) ( ) 827cos1037

u v− =

Ans: E Learning Objective: Calculate exact value of expression using sum or difference formula Section: 5.4



70. Write the given expression as an algebraic expression.

A)

B)

C)

D)

E)

Ans: D Learning Objective: Write trig expression as an algebraic expression Section: 5.4

71. Simplify the given expression algebraically.

A)

B)

C)

D)

E)

Ans: B Learning Objective: Simplify trigonometric expression using sum and difference formulas Section: 5.4



72. Simplify the given expression algebraically.

A)

B)

C)

D)

E)

Ans: D Learning Objective: Simplify trig expression using sum and difference formulas Section: 5.4


I. ( ) ( ) ( )sin + sin – 2sinx y x y x+ =

II. ( ) ( ) ( )sin + sin – 2sinx x xπ π− =

III. ( ) ( ) ( ) ( )sin + sin – 2sin sinx y x y x y+ = A) II and II are the only identities. D) I is the only identity. B) I and III are the only identities. E) III is the only identity. C) None are identities.

Ans: C Learning Objective: Verify an identity using sum and difference formulas Section: 5.4

74. Verify the given identity.

Ans:

Learning Objective: Verify an identity using sum and difference formulas Section: 5.4



75. Find all solutions of the given equation in the interval [ )0, 2π .

A)

B)

C)

D)

E)

Ans: C Learning Objective: Solve trig equation with sum/difference formulas Section: 5.4



76. Use the figure below to determine the exact value of the given function.

θ

3

2

θ

3

2

A)

B)

C)

D)

E)

Ans: E Learning Objective: Calculate exact value of a trigonometric function using a right triangle Section: 5.5



77. Use the graph below of the function to approximate the solutions to ( ) ( )2cos 2 cos 0x x− = in the interval [ )0, 2 .π Round your answers to one decimal.

A) 0.6, 1.0, 1.5, 4.8 D) 0.6, 2.1, 4.2, 5.7 B) 1.0, 1.5, 4.8, 5.7 E) 0.6, 1.5, 4.2, 6.3 C) 1.0, 2.1, 4.2, 5.7

Ans: D Learning Objective: Approximate solutions of trigonometric equation with a graph Section: 5.5



78. Find the exact solutions of the given equation in the interval [ )0, 2π .

A)

B)

C)

D)

E)

Ans: D Learning Objective: Solve trigonometric equation Section: 5.5



79. Find the exact solutions of the given equation in the interval [ )0, 2π .

A)

B)

C)

D)

E) 0x = Ans: B Learning Objective: Solve trigonometric equation Section: 5.5

80. Use a double-angle formula to find the exact value of cos 2u when

7sin , where25 2

u uπ π= < < .

A) 478cos 2 –625

u = D) 527cos 2

625u =

B) 168cos 2625

u = E) 1152cos 2 –

625u =

C) 336cos 2625

u =

Ans: D Learning Objective: Calculate exact value of a trigonometric function using a double-angle formula Section: 5.5



81. Use a double-angle formula to find the exact value of tan 2u when 12 3cos , where13 2

u u ππ= − < < .

A) 5tan 2 –6

u = D) 130tan 2

119u =

B) 312tan 2 –25

u = E) 5tan 2

12u =

C) 120tan 2119

u =

Ans: C Learning Objective: Calculate exact value of a trigonometric function using a double-angle formula Section: 5.5

82. Use a double angle formula to rewrite the following expression.

( ) ( )–14sin cosx x

A) ( )sin –14x D) ( )–7sin 2x B) ( )2sin –7x E) ( )cos –14x C) ( )–7 cos 2x

Ans: D Learning Objective: Rewrite expression as a double angle Section: 5.5

83. Use a double angle formula to rewrite the given expression.

28cos 4x − A) 4cos 2x B) 8cos 2x C) 2cos 4x D) 4cos 4x E) 2cos8x Ans: A Learning Objective: Rewrite expression as a double angle Section: 5.5




I. ( ) ( ) ( )( )4 1cos 1+ 4cos 2 + cos 44

x x x=

II. ( ) ( ) ( )( )4 1cos 3+ 4sin 2 – sin 48

x x x=

III. ( ) ( ) ( )( )4 1cos 3+ 4cos 2 + cos 48

x x x= A) None are identities. D) I and III are the only identities. B) III is the only identity. E) I, II, and III are identities. C) I and II are the only identities.

Ans: B Learning Objective: Verify a trigonometric identity Section: 5.5

85. Use the power-reducing formulas to rewrite the given expression in terms of the first

power of the cosine.

A)

B)

C)

D)

E)

Ans: E Learning Objective: Rewrite expression using power-reducing formulas Section: 5.5



86. Use the figure below to find the exact value of the given trigonometric expression.

sin2θ

θ 6 8 (figure not necessarily to scale)

A) 3

10 B) 3

2 C) 3 10

10 D) 10

10 E) 1

10 10

Ans: D Learning Objective: Calculate exact value of a trigonometric function using a right triangle Section: 5.5



87. Use the figure below to find the exact value of the given trigonometric expression.

θ

7

24

θ

7

24

A)

B)

C)

D)

E)

Ans: C Learning Objective: Calculate exact value of a trigonometric function using a right triangle Section: 5.5

88. Use the half-angle formulas to determine the exact value of the following.

( )cos 22.5

A) 2 + 3–

2 B) 2 – 2

2 C) 2 – 2–

2 D) 3 – 3

2 E) 2 + 2

2

Ans: E Learning Objective: Calculate exact value of a trigonometric function using a half-angle formula Section: 5.5



89. Use the half-angle formulas to determine the exact value of the given trigonometric expression.

A)

B)

C)

D)

E)

Ans: A Learning Objective: Calculate exact value of a trigonometric function using a half-angle formula Section: 5.5

90. Use the half-angle formula to simplify the given expression.

1 cos 202

x+

A) cos 40x B) cos10x C) cos 20x D) cos80x E) cos5x Ans: B Learning Objective: Rewrite expression using half-angle formulas Section: 5.5




A)

B)

C)

D)

E)

Ans: C Learning Objective: Solve trigonometric equation using half-angle formulas Section: 5.5

92. Use the product-to-sum formula to write the given product as a sum or difference.

8sin sin8 8π π

A) 4sin

16π

D) –4sin

16π

B) 4 4cos

4π−

E) 4sin 4cos

8 8π π+

C) 4 4cos

16π+

Ans: B Learning Objective: Rewrite expression with a product-to-sum formula Section: 5.5



93. Use the product-to-sum formula to write the given product as a sum or difference.

4sin cos12 12π π

A) 2sin 2cos

12 12π π+

D) 2 2cos

24π−

B) 2sin

6π

E) –2sin

24π

C) 2 2cos

24π+

Ans: B Learning Objective: Rewrite expression with a product-to-sum formula Section: 5.5

94. Use the product-to-sum formulas to write the expression below as a sum or difference.

( ) ( )sin 6 cos 4θ θ

A) ( ) ( )( )1 cos 2 cos 102

θ θ+ D) ( ) ( )( )1 cos 2 cos 10

2θ θ−

B) ( ) ( )( )1 sin 2 cos 102

θ θ+ E) ( ) ( )( )1 sin 10 sin 2

2θ θ−

C) ( ) ( )( )1 sin 10 sin 22

θ θ+

Ans: C Learning Objective: Rewrite expression with a product-to-sum formula Section: 5.5

95. Use the sum-to-product formulas to write the given expression as a product.

sin 9 sin 7θ θ− A) 2sin 8 cosθ θ D) 2cos8 cosθ θ− B) 2cos8 cosθ θ E) 2cos8 sinθ θ C) 2sin 8 sinθ θ−

Ans: E Learning Objective: Rewrite expression with a product-to-sum formula Section: 5.5

96. Use the sum-to-product formulas to write the given expression as a product.

cos 6 cos 4θ θ− A) 2sin 5 sinθ θ− D) 2sin 5 cosθ θ B) 2cos5 cosθ θ E) 2cos5 cosθ θ− C) 2cos5 sinθ θ

Ans: A Learning Objective: Rewrite expression with a sum-to-product formula Section: 5.5



97. Use the sum-to-product formulas to find the exact value of the given expression.

A)

B)

C)

D)

E)

Ans: C Learning Objective: Evaluate expression using sum-to-product formulas Section: 5.5


A)

B)

C)

D)

E)

Ans: D Learning Objective: Solve trigonometric equations using sum-to-product formulas Section: 5.5




Ans:

Learning Objective: Verify an identity using sum-to-product formulas Section: 5.5


I. ( ) ( )

( ) ( )cos 4 – cos 2– sin

2sin 3x x

xx

=

II. ( ) ( )( ) ( ) ( )cos 4 – cos

– sin 2sin 3 sin

x xx

x x=

−

III. ( ) ( )( ) ( ) ( )cos 6 – cos 2

– sin 3sin 4 sin 2

x xx

x x=

+

A) I is the only identity. D) I and II are the only identities. B) II and II are the only identities. E) III is the only identity. C) None are identities.

Ans: A Learning Objective: Verify an identity using sum-to-product formulas Section: 5.5




Ans:

Learning Objective: Verify an identity using sum-to-product formulas Section: 5.5

chapter 5: analytic trigonometry - crunchy math -...

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