review chapters 13-14€¦ · b. ∠p =10°, q ≈2.6, p ≈15.2 d ... a 15-m long ladder rests...

Name: ________________________ Class: ___________________ Date: __________ ID: A

2

Review Chapters 13-14

Multiple ChoiceIdentify the choice that best completes the statement or answers the question.

____ 1. Solve ΔPQ R by using the measurements ∠PQ R = 90°, ∠Q RP = 80°, and r = 15. Round measures of sides to the nearest tenth and measures of angles to the nearest degree.

a. ∠P = 10°, q ≈ 15.2, p ≈ 2.6 c. ∠P = 10°, q ≈ 15.2, p ≈ 14.8b. ∠P = 10°, q ≈ 2.6, p ≈ 15.2 d. ∠P = 10°, q ≈ 85.1, p ≈ 14.8

____ 2. A 15-m long ladder rests against a wall at an angle of 60° with the ground. How far is the foot of the ladder from the wall?a. 7.5 m c. 17.3 mb. 12.9 m d. 30 m

____ 3. The upper part of a tree, broken by wind, makes an angle of 38° with the ground. The horizontal distance from the root of the tree to the point where the top of the tree meets the ground is 20 meters. Find the height of the tree before it was broken.a. 9.754 m c. 25.380 mb. 15.626 m d. 41.006 m

____ 4. Two boys are on opposite sides of a tower. They sight the top of the tower at 33° and 24° angles of elevation respectively. If the height of the tower is 100 m, find the distance between the two boys.a. 378.59 m c. 153.99 mb. 224.60 m d. 70.61 m

____ 5. An engineer stands 200 feet from a tower and sights the top of the tower at a 45° angle of elevation. Find the height of the tower.a. 100 feet c. 200 feetb. 275 feet d. 141.42 feet

Name: ________________________ ID: A

2

____ 6. A kite at a height of 75 meters from the ground is attached to a string inclined at 60° to the horizontal. Find the length of the string to the nearest meter.a. 43 m c. 130 mb. 87 m d. 150 m

____ 7. A preprogrammed workout on a treadmill consists of intervals walking at various rates and angles of incline. A 2% incline means 2 units of vertical rise for every 100 units of horizontal run. At what angle, with respect to the horizontal, is the treadmill bed when set to a 20% incline? Round to the nearest degree.a. 4° b. 6° c. 11° d. 20°

Rewrite the radian measure in degrees.

____ 8. π

45a. 2° c. 4°b. 40° d. 4π °

Rewrite the degree measure in radians.

____ 9. 90°

a. 360π c.2π

b. 114.65π d.π

2

____ 10. Find one angle with positive measure and one angle with negative measure coterminal with an angle of 166°.a. 256°, –76° c. 526°, –194°b. 526°, –76 d. 488°, –14°

Find the value of the given trigonometric function.

____ 11. cos 1500°( )

a. 12 c. 1

2

b.3

2 d. 3

____ 12. tan −1740°( )

a.3

2 c. 3

b. 13

d. 12

Name: ________________________ ID: A

3

Find the exact values of the remaining five trigonometric functions of θ.

____ 13. Suppose θ is an angle in the standard position whose terminal side is in Quadrant IV and cotθ = −2.

a. sinθ = − 15

, cosθ = 25

, cscθ = − 5, secθ =5

2 , tanθ = −12

b. sinθ = 15

, cosθ = 25

, cscθ = 5, secθ =5

2 , tanθ = 12

c. sinθ = − 5, cosθ =5

2 , cscθ = − 15

, secθ = 25

, tanθ = −12

d. sinθ = 15

, cosθ = − 25

, cscθ = − 5, secθ = −5

2 , tanθ = 12

____ 14. Suppose θ is an angle in the standard position whose terminal side is in Quadrant I and tanθ = 6011.

a. sinθ = −6061, cosθ = −11

61, cscθ = −6160, secθ = −61

11 , cotθ = −1160

b. sinθ = 6160, cosθ = 61

11, cscθ = 6061, secθ = 11

61 , cotθ = 6011

c. sinθ = 6061, cosθ = 11

61, cscθ = 6160, secθ = 61

11 , cotθ = 1160

d. sinθ = −6061, cosθ = −11

61, cscθ = −6160, secθ = 61

11 , cotθ = −1160

____ 15. Suppose θ is an angle in the standard position whose terminal side is in Quadrant III and cosθ = −5

3 .

a. sinθ = 23, cscθ = 3

2, secθ = − 35

, tanθ = − 25

, and cotθ = −5

2

b. sinθ = 23, cscθ = 3

2, secθ = − 35

, tanθ = − 25

, and cotθ = −5

2

c. sinθ = 32, cscθ = 2

3, secθ = − 35

, tanθ = −5

2 , and cotθ = − 25

d. sinθ = −23, cscθ = −3

2, secθ = − 35

, tanθ = 25

, and cotθ =5

2

Name: ________________________ ID: A

4

____ 16. Suppose θ is an angle in the standard position whose terminal side is in Quadrant IV and cotθ = −2 2 .

a. sinθ = −13, cosθ =

2 23 , cscθ = −3, secθ = 3

2 2, tanθ = − 1

2 2

b. sinθ = −13, cosθ = −

2 23 , cscθ = −3, secθ = − 3

2 2, tanθ = 1

2 2

c. sinθ = 13, cotθ =

2 23 , cscθ = 3, secθ = 3

2 2, tanθ = 1

2 2

d. sinθ = −3, cosθ = 32 2

, cscθ = −13, secθ =

2 23 , tanθ = − 1

2 2

____ 17. Suppose θ is an angle in the standard position whose terminal side is in Quadrant IV and sinθ = −3

2 .

a. cosθ = 12, cscθ = − 2

3, secθ = 2, tanθ = − 3 , cotθ = − 1

3

b. cosθ = 12, cscθ = 2

3, secθ = 2, tanθ = 3, cotθ = 1

3

c. cosθ = −12, cscθ = 2

3, secθ = −2, tanθ = − 3, cotθ = − 1

3

d. cosθ = 2, cscθ = − 23

, secθ = 12, tanθ = − 1

3, cotθ = − 3

____ 18. Suppose θ is an angle in the standard position whose terminal side is in Quadrant I and cscθ =4 7

7 .

a. sinθ =7

4 , cosθ = 34, secθ = 4

3, tanθ =7

3 , cotθ =3 7

7

b. sinθ = 34, cosθ =

74 , sec secθ = 4

3, tanθ =7

3 , cotθ =3 7

7

c. sinθ = −7

4 , cosθ = −34, secθ = −4

3, tanθ = −7

3 , cotθ = −3 7

7

d. sinθ = −7

4 , cosθ = 34, secθ = 4

3, tanθ = −7

3 , cotθ = −3 7

7

Name: ________________________ ID: A

5

Determine whether the given triangle has no solution, one solution or two solutions. Then solve the triangle. Round measures of sides to the nearest tenth and measures of angles to the nearest degree.

____ 19.

A = 112°, a = 7, b = 4a. one solution; c ≈ 7; B = 32°; C = 112°b. no solutionc. one solution; c ≈ 4.4; B = 36°; C = 32°d. one solution; c ≈ 4.4; B = 32°; C = 36°

Determine whether each triangle should be solved by beginning with the Law of Sines or the Law of Cosines. Then solve each triangle. Round measures of sides to the nearest tenth and measures of angles to the nearest degree.

____ 20.

a = 15, b = 14, c = 11a. Law of Cosines; A ≈ 63°, B ≈ 73°, C ≈ 44°b. Law of Cosines; A ≈ 73°, B ≈ 63°, C ≈ 44°c. Law of Sines; A ≈ 44°, B ≈ 63°, C ≈ 73°d. Law of Sines; A ≈ 73°, B ≈ 63°, C ≈ 44°

Name: ________________________ ID: A

6

____ 21.

A = 90°, b = 9, a = 18a. Law of Sines; B ≈ 30°, C ≈ 60°, c ≈ 15.6b. Law of Sines; B ≈ 60°, C ≈ 30°, c ≈ 15.6c. Law of Cosines; B ≈ 61°, C ≈ 29°, c ≈ 15.6d. Law of Cosines; B ≈ 29°, C ≈ 61°, c ≈ 15.6

____ 22.

A = 50°, b = 11, a = 16a. Law of Sines; B ≈ 32°, C ≈ 98°, c ≈ 20.7b. Law of Cosines; B ≈ 100°, C ≈ 30°, c ≈ 20.7c. Law of Sines; B ≈ 98°, C ≈ 32°, c ≈ 20.7d. Law of Cosines; B ≈ 30°, C ≈ 100°, c ≈ 20.7

____ 23.

a = 19, b = 20, C = 63°a. Law of Sines; c ≈ 33, A ≈ 31°, B ≈ 86°b. Law of Cosines; c ≈ 33, A ≈ 31°, B ≈ 86°c. Law of Sines; c ≈ 20.4, A ≈ 61°, B ≈ 56°d. Law of Cosines; c ≈ 20.4, A ≈ 56°, B ≈ 61°

Name: ________________________ ID: A

7

The given point P is located on the unit circle. Find sinθ and cosθ .

____ 24. P 1161 , 60

61Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃

a. sinθ = 1161; cosθ = 60

61 c. sinθ = −6061; cosθ = −11

61

b. sinθ = 6061; cosθ = 11

61 d. sinθ = −1161; cosθ = −60

61

____ 25. P 20101 , 99

101Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃

a. sinθ = 20101; cosθ = 99

101 c. sinθ = 20101; cosθ = − 99

101

b. sinθ = 99101; cosθ = 20

101 d. sinθ = − 99101; cosθ = 20

101

____ 26. Find the exact value of the function sin −390°( )

a. 0.5 c.3

2

b. −0.5 d.2

2

____ 27. Find the value of cot (Cos −1 23). Round to the nearest hundredth.

a. 0.87 c. 1.12b. 0.89 d. 1.00

Name: ________________________ ID: A

8

Find the amplitude, if it exists, and period of the function. Then, graph the function.

____ 28. y = 118 tanθ

a.

amplitude: 118; period: 2π

c.

amplitude: 118; period: π

b.

amplitude: does not exist; period: π

d.

amplitude: does not exist; period: π

A person’s resting blood pressure is 115 over 86. This means that the blood pressure oscillates between a maximum of 115 and a minimum of 86. The person’s resting heart rate is 60 beats per minute. Let P represent the blood pressure and t represent the time in seconds.

____ 29. Write a sine function for the blood pressure P as a function of time, t, in seconds.a. p = 14.5sin2π t + 14.5 c. p = 14.5sinπ t + 100.5b. p = −14.5sin2π t + 100.5 d. p = 14.5sin2π t + 100.5

Name: ________________________ ID: A

9

State the amplitude, period, and phase shift for the function. Then, graph the function.

____ 30. y = 113 tan θ + 30°( )

a.

amplitude = 113; period = 180°;

phase shift = –30°

c.

amplitude = does not exist; period = 180°; phase shift = 30°

b.

amplitude = does not exist; period = 180°; phase shift = –30°

d.

amplitude = does not exist; period = 180°; phase shift = –30°

____ 31. Find the value of cscθ , if cosθ = −18; 180° < θ < 270°.

a. −8 c. −8

63

b. 863

d. − 863

Name: ________________________ ID: A

10

Verify which of the following are identities.

____ 32. 1) 8 cot2θcsc θ sec2θ = 7tanθ cosθ csc2θ

2) 7 cot2θcsc θ sec2θ = 7tanθ cosθ csc2θ

a. Only the second equation is an identity.b. Both the equations are identities.c. Only the first equation is an identity.d. None of the equations are identities.

____ 33. 1) sin 180° + θ( ) = −2cosθ2) cos 180° + θ( ) = −4sinθ a. Both the equations are identities.b. Only the first equation is an identity.c. Only the second equation is an identity.d. None of the equations are identities.

____ 34. 1) sin θ + π4

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃ =

12

sinθ + cosθ( )

2) cos θ − π4

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃ =

12

sinθ + cosθ( )

a. Both the equations are identities.b. Only the first equation is an identity.c. Only the second equation is an identity.d. None of the equations are identities.

____ 35. 1) sin 45° + θ( ) + cos 45° − θ( ) = sinθ + cosθ 2) cos 60° + θ( ) − sin 60° − θ( ) = cos2θ + tanθa. Both the equations are identities.b. Only the first equation is an identity.c. Only the second equation is an identity.d. None of the equations are identities.

____ 36. 1) sin α + βÊËÁÁ

ˆ¯̃̃ =

1− tanα tanβsinα

2) cos α + βÊËÁÁ

ˆ¯̃̃ =

2− cotα cotβ2sinα sinβ


Name: ________________________ ID: A

11

____ 37. 1) sin θ + 2π4

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃ = 2 sinϑ cosθ

2) cos θ − π3

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃ =

32

cosθ − sinθ( )


____ 38. Solve 2tanθ = 2cotθ for all values of θ if θ is measured in degrees.a. 45° + k ⋅ 90° c. 45° − 2k ⋅ 180°b. 45° − k ⋅ 180° d. 45° + k ⋅ 360°

The length of the shadow S of the tallest tower among the Watts Towers, United States, depends upon the angle of inclination of the Sun, θ. The height of the tallest tower is 99 feet.

____ 39. Express S as a function of θ.

a. S = tanθ99 c. S = 99

tanθb. S = 99secθ d. S = 99tanθ

Name: ________________________ ID: A

12

The height of a wave created by wind can be modeled using y = 2h sin3πtp

, where h is the maximum height of

the wave in feet, p is the period in seconds, and t is the propagation of the wave in seconds.

____ 40. If h = 1 and p = 5 seconds, write the equation for the wave and draw its graph over a 10-second interval.a.

y = 2 sin 3πt5

c.

y = sin 3πt5

b.

y = 2 sin 3πt

d.

y = 2 sin 5πt3

____ 41. How many times over the first 5 seconds does the graph predict the wave to be 1 foot high?

a. 1 c. 4b. 2 d. 6

Name: ________________________ ID: A

13

The length of the shadow S of the tallest television transmitting tower in North Dakota, depends upon the angle of inclination of the Sun, θ. The height of the tower is 2,070 feet.


a. S =2,070tanθ c. S = tanθ

2,070b. S = 2,070secθ d. S = 2,070tanθ

____ 43. Find the angle of inclination θ that will produce a shadow 800 feet long.a. about –69° c. about 21°b. about 71° d. about 69°

The length of the shadow S of the Sears Tower in Chicago depends upon the angle of inclination of the Sun, θ. The height of the tower is 1,454 feet.


a. S = 1,454 tanθ c. S = tanθ1,454

b. S = 1,454 secθ d. S =1,454tanθ

Name: ________________________ ID: A

14

For a short time after a wave is created by wind, the height of the wave can be modeled using y = a sin 2πtT

,

where a is the amplitude and T is the period of the wave in seconds.

____ 45. If a = 2 and T = 2 seconds, write the equation for the wave and draw its graph over a 10-second interval.a.

y = sin 2πt2

c.

y = 2sin 2πt2

b.

y = 2sin2πt

d.

y = 2sin 2πt2

____ 46. How many times over the first 5 seconds does the graph predict the wave to be 2 feet high?

a. 3 c. 6b. 4 d. 10

Name: ________________________ ID: A

15

Essay

47. In the figure, x = 4y.a. What is the value of a?b. Find the value of all the angles of the triangle.c. If x = 2y, then find the value of a.

48. 2a + 4b + 3c – d = 322b + 3d = 184c + d = 12If c = 2, find the values of:a. db. bc. a

49. If m is a positive integer, and 3m + 1 equals a prime number that is less than 20, then find the following:a. The lowest possible value of 3m + 1.b. The maximum possible value of 3m + 1.

50. If 3a − 7b = 0 and c = 4b, what is the ratio of:a. b to c?b. a to c?

ID: A

1

Review Chapters 13-14Answer Section

MULTIPLE CHOICE

1. ANS: AIf the measures of one side and one acute angle are known, you can determine the measures of all sides and angles of the triangle by using trigonometric functions.

FeedbackA Correct!B Did you interchange the values of p and q?C Use the measures of the side and acute angle to find the missing measures.D Did you use the trigonometric functions to find the missing measures?

PTS: 1 DIF: Advanced REF: Page 707 OBJ: 13-1.2 Solve right triangles.TOP: Solve right triangles. KEY: Solve Triangles | Right Triangles

2. ANS: AWrite an equation using a trigonometric function that involves the ratio of length and 15.

FeedbackA Correct!B Did you write an equation using a trigonometric function that involves the ratio of the

length of the ladder and the distance of the foot of the ladder from the wall?C Use cos 60 to find how far is the foot of the ladder from the wall.D Did you use the correct trigonometric function?

PTS: 1 DIF: Basic REF: Page 707 OBJ: 13-1.3 Solve real-world problems involving right triangles. TOP: Solve real-world problems involving right triangles. KEY: Right Triangles | Real-World Problems

3. ANS: DWrite an equation using a trigonometric function that involves the ratio of l and 20.

FeedbackA Did you use the correct trigonometric function?B Did you write an equation using a trigonometric function?C Use the tan function to find the height of the lower part of the tree.D Correct!

PTS: 1 DIF: Average REF: Page 707 OBJ: 13-1.3 Solve real-world problems involving right triangles. TOP: Solve real-world problems involving right triangles. KEY: Right Triangles | Real-World Problems

ID: A

2

4. ANS: AWrite an equation using a trigonometric function.

FeedbackA Correct!B Did you write an equation using a trigonometric function?C Use the tan function to find the distance between the two boys.D Did you use the correct trigonometric function?

PTS: 1 DIF: Advanced REF: Page 707 OBJ: 13-1.3 Solve real-world problems involving right triangles. TOP: Solve real-world problems involving right triangles. KEY: Right Triangles | Real-World Problems

5. ANS: CWrite an equation using a trigonometric function that involves the ratio of the height of the tower and the distance of the engineer from the tower.

FeedbackA Did you write an equation using a trigonometric function?B Use the tan function to find the height of the tower.C Correct!D Did you use the correct trigonometric function?


6. ANS: BWrite an equation using a trigonometric function that involves the ratio of the height of the kite from the ground and the length of the string.

FeedbackA Did you write an equation using a trigonometric function?B Correct!C Use sin 60 to find the length of the string.D Write an equation using trigonometric functions and then find the length.


ID: A

3

7. ANS: CUse the tan−1 function to find the measure of the required angle.

FeedbackA Did you use the correct trigonometric function to determine the required angle?B When one of the trigonometric ratios is known, use its inverse to find the measure of the

required angle.C Correct!D Use the inverse of the tan function to find the measure of the required angle.

PTS: 1 DIF: Advanced REF: Page 707 OBJ: 13-1.3 Solve real-world problems involving right triangles. TOP: Solve real-world problems involving right triangles. KEY: Right Triangles | Real-World Problems

8. ANS: C

To rewrite the radian measure of an angle in degrees, multiply the number of radians by 180°

π radians.

FeedbackA One radian is around 57 degrees.B One degree is about 0.0175 radian.C Correct!D Did you multiply the number of radians correctly by the conversion factor?

PTS: 1 DIF: Basic REF: Page 712 OBJ: 13-2.1 Change radian measure to degree measure. TOP: Change radian measure to degree measure. KEY: Radian Measure | Degree Measure

9. ANS: D

To rewrite the degree measure of an angle in radians, multiply the number of degrees by π radians

180°.

FeedbackA Did you multiply the number of degrees correctly by the conversion factor?B One radian is about 57 degrees.C One degree is about 0.0175 radians.D Correct!

PTS: 1 DIF: Average REF: Page 713 OBJ: 13-2.2 Change degree measure to radian measure. TOP: Change degree measure to radian measure. KEY: Radian Measure | Degree Measure

ID: A

4

10. ANS: CIn degree measure, coterminal angles differ by an integral multiple of 360°.

FeedbackA When two angles in the standard position have the same terminal sides, they are called

coterminal angles.B In degree measure, coterminal angles differ by an integral multiple of 360 degrees.C Correct!D Did you add or subtract the given angle with an integral multiple of 360 degrees?

PTS: 1 DIF: Basic REF: Page 713 OBJ: 13-2.3 Identify coterminal angles.TOP: Identify coterminal angles. KEY: Coterminal Angles

11. ANS: AFirst, find the reference angle θ ′. Then, find the value of the trigonometric function for θ ′. Then, using the quadrant in which the terminal side of θ lies, determine the sign of the trigonometric function value of θ.

FeedbackA Correct!B Did you find the reference angle of the given angle?C Use a reference angle to find the value of the given trigonometric function.D Find the cos of the given angle, not tan.

PTS: 1 DIF: Average REF: Page 723 OBJ: 13-3.1 Find values of sine and cosine for general angles. TOP: Find values of sine and cosine for general angles. KEY: Sine | Cosine

12. ANS: CFirst, find the reference angle θ ′. Then, find the value of the trigonometric function for θ ′. Then, using the quadrant in which the terminal side of θ lies, determine the sign of the trigonometric function value of θ.

FeedbackA Did you find the reference angle of the given angle?B Find tan of the given angle, not cot.C Correct!D Use a reference angle to find the value of the given trigonometric function.

PTS: 1 DIF: Average REF: Page 723 OBJ: 13-3.3 Find values of tangent and cotangent for general angles. TOP: Find values of tangent and cotangent for general angles. KEY: Tangent | Cotangent

ID: A

5

13. ANS: AIf the quadrant that contains the terminal side of θ in the standard position and the exact value of one trigonometric function of θ are known, then the values of the other trigonometric functions of θ can be obtained using the function definitions.

FeedbackA Correct!B The angle is in Quadrant IV and not in Quadrant I.C Use the function definitions to find the remaining five trigonometric functions.D Did you use the correct signs of the trigonometric functions for Quadrant IV?

PTS: 1 DIF: Advanced REF: Page 723 OBJ: 13-3.4 Use reference angles to find values of trigonometric functions.TOP: Use reference angles to find values of trigonometric functions. KEY: Reference Angles | Trigonometric Functions

14. ANS: CIf the quadrant that contains the terminal side of θ in the standard position and the exact value of one trigonometric function of θ are known, then the values of the other trigonometric functions of θ can be obtained using the function definitions.

FeedbackA Did you use the correct signs of the trigonometric functions for Quadrant I?B Use function definitions to find the remaining five trigonometric functions.C Correct!D The angle is in Quadrant I and not in Quadrant IV.


15. ANS: DIf the quadrant that contains the terminal side of θ in the standard position and the exact value of one trigonometric function of θ are known, then the values of the other trigonometric functions of θ can be obtained using the function definitions.

FeedbackA Did you use the correct signs of the trigonometric functions for Quadrant III?B The angle is in Quadrant III and not in Quadrant II.C Use function definitions to find the remaining five trigonometric functions.D Correct!


ID: A

6


FeedbackA Correct!B Did you use the correct signs of the trigonometric functions for Quadrant IV?C The angle is in Quadrant IV and not in Quadrant I.D Use function definitions to find the remaining five trigonometric functions.



FeedbackA Correct!B The angle is in Quadrant IV and not in Quadrant I.C Did you use the correct signs of the trigonometric functions for Quadrant IV?D Use function definitions to find the remaining five trigonometric functions.



FeedbackA Correct!B Use function definitions to find the remaining five trigonometric functions.C Did you use the correct signs of the trigonometric functions for Quadrant I?D The angle is in Quadrant I and not in Quadrant IV.


ID: A

7

19. ANS: DDetermine whether the given triangle has zero, one or two solutions. Find the measure of angle C and the value of c.

FeedbackA Did you calculate the value of C correctly?B Did you use the Law of Sines correctly?C Did you interchange the values of angles B and C?D Correct!

PTS: 1 DIF: Advanced REF: Page 731 OBJ: 13-4.2 Determine whether a triangle has one, two or no solutions. TOP: Determine whether a triangle has one, two or no solutions. KEY: Solve Triangles

20. ANS: BWhen the measures of three sides are given, first use the Law of Cosines to find the measure of the largest angle. Then, use the Law of Sines to find the other angles.

FeedbackA Did you interchange the measures of the angles?B Correct!C Did you find the correct angles?D What is the Law of Cosines?

PTS: 1 DIF: Average REF: Page 736 OBJ: 13-5.1 Solve problems by using the Law of Cosines. TOP: Solve problems by using the Law of Cosines. KEY: Solve Problems | Law of Cosines

21. ANS: AUse the Law of Sines when two sides and an angle opposite one of them are given.

FeedbackA Correct!B Did you interchange the angles?C What is the Law of Sines?D Did you use the correct law?

PTS: 1 DIF: Average REF: Page 736 OBJ: 13-5.2 Determine whether a triangle can be solved by first using the Law of Sines or the Law of Cosines. TOP: Determine whether a triangle can be solved by first using the Law of Sines or the Law of Cosines.KEY: Solve Triangles | Law of Sines | Law of Cosines

ID: A

8

22. ANS: AUse the Law of Sines when two sides and an angle opposite one of them are given.

FeedbackA Correct!B What is the Law of Sines?C Did you interchange the angles?D Did you use the correct law?

PTS: 1 DIF: Average REF: Page 736 OBJ: 13-5.2 Determine whether a triangle can be solved by first using the Law of Sines or the Law of Cosines. TOP: Determine whether a triangle can be solved by first using the Law of Sines or the Law of Cosines.KEY: Solve Triangles | Law of Sines | Law of Cosines

23. ANS: DWhen the measures of two sides and their included angle are given, use the Law of Cosines.

FeedbackA Did you begin with the correct law?B Did you use the correct formula?C Did you interchange the values of the angles?D Correct!

PTS: 1 DIF: Average REF: Page 736 OBJ: 13-5.1 Solve problems by using the Law of Cosines. TOP: Solve problems by using the Law of Cosines. KEY: Solve Problems | Law of Cosines

24. ANS: BIf the terminal side of an angle θ in the standard position intersects the unit circle at P (x, y), then cosθ = x and sinθ = y.

FeedbackA Did you write the answers in the correct order?B Correct!C Did you change the sign of the coordinates?D Check the sign of the coordinates.

PTS: 1 DIF: Basic REF: Page 743 OBJ: 13-6.1 Define and use the trigonometric functions based on the unit circle.TOP: Define and use the trigonometric functions based on the unit circle.KEY: Trigonometric Functions | Unit Circle

ID: A

9

25. ANS: BIf the terminal side of an angle θ in the standard position intersects the unit circle at P (x, y), then cosθ = x and sinθ = y.

FeedbackA Did you write the answers in the correct order?B Correct!C Did you change the sign of the coordinates?D Check the sign of the coordinates.

PTS: 1 DIF: Basic REF: Page 743 OBJ: 13-6.1 Define and use the trigonometric functions based on the unit circle.TOP: Define and use the trigonometric functions based on the unit circle.KEY: Trigonometric Functions | Unit Circle

26. ANS: BFind the value of the sine of the angle in degrees.

FeedbackA How do you determine the sign of the function value?B Correct!C Where is the terminal side of the angle?D What is the reference angle?

PTS: 1 DIF: Basic REF: Page 743 OBJ: 13-6.2 Find the exact values of trigonometric functions of angles. TOP: Find the exact values of trigonometric functions of angles. KEY: Trigonometric Functions

27. ANS: BEvaluate the inverse trigonometric function to obtain an angle measure. Find the value of the cotangent of that angle measure.

FeedbackA Did you find the cotangent value correctly?B Correct!C Did you find the inverse of the correct trigonometric function?D Did you calculate the answer correctly?

PTS: 1 DIF: Basic REF: Page 749 OBJ: 13-7.2 Find values of expressions involving trigonometric functions.TOP: Find values of expressions involving trigonometric functions. KEY: Trigonometric Functions

ID: A

10

28. ANS: DDetermine the amplitude and period of the function and use them to plot the graph.

FeedbackA Did you calculate the amplitude and period of the function correctly?B You have plotted the incorrect amplitude.C Did you calculate the amplitude of the function correctly?D Correct!

PTS: 1 DIF: Basic REF: Page 767 OBJ: 14-1.4 Find the amplitude and period of variation of tangent and cotangent functions.TOP: Find the amplitude and period of variation of tangent and cotangent functions.KEY: Amplitude | Period | Tangent | Cotangent

29. ANS: DDetermine the vertical shift, amplitude, and period of the function. Then, substitute these values in the equation P = asin[b(t− h)] + k , where a is the amplitude, b is the period of the function, t is the time in seconds, h is the phase shift, and k is the vertical shift.

FeedbackA Midline is the mean of the maximum and minimum values.B The amplitude cannot be a negative value.C Did you calculate the period of the function correctly?D Correct!

PTS: 1 DIF: Advanced REF: Page 774 OBJ: 14-2.1 Graph horizontal translations of trigonometric graphs and find phase shifts.TOP: Graph horizontal translations of trigonometric graphs and find phase shifts.KEY: Horizontal Translations | Trigonometric Graphs | Phase Shift

30. ANS: BDetermine the amplitude, period, and phase shift for the function and use them to plot the graph.

FeedbackA Did you calculate the amplitude of the function correctly?B Correct!C Did you calculate the phase shift of the function correctly?D You have plotted the incorrect period.

PTS: 1 DIF: Advanced REF: Page 774 OBJ: 14-2.2 Graph vertical translations of trigonometric graphs. TOP: Graph vertical translations of trigonometric graphs. KEY: Vertical Translations | Trigonometric Graphs

ID: A

11

31. ANS: CApply the Pythagorean and reciprocal identities.

FeedbackA This is the secant value.B You have used an incorrect sine value.C Correct!D Did you apply the Pythagorean identity correctly?

PTS: 1 DIF: Average REF: Page 779 OBJ: 14-3.1 Use identities to find trigonometric values. TOP: Use identities to find trigonometric values. KEY: Trigonometric Identities

32. ANS: AUse the quotient and reciprocal identities to solve the equations.

FeedbackA Correct!B Did you transform both sides into a common form? !C Did you apply the reciprocal or Pythagorean identity correctly in the second equation?D Did you apply the correct identities in both the equations?

PTS: 1 DIF: Average REF: Page 784 OBJ: 14-4.2 Verify trigonometric identities by transforming each side of the equation into the same form.TOP: Verify trigonometric identities by transforming each side of the equation into the same form.KEY: Trigonometric Identities

33. ANS: DApply the sum of angles formula to determine if the equations are identities.

FeedbackA Did you apply the sum of angles formula correctly in both the equations?B Did you apply the sum of angles formula correctly in the first equation?C Did you apply the sum of angles formula correctly in the second equation?D Correct!

PTS: 1 DIF: Average REF: Page 789 OBJ: 14-5.2 Verify identities by using sum and difference formulas. TOP: Verify identities by using sum and difference formulas. KEY: Trigonometric Identities | Sum and Difference Formulas

ID: A

12

34. ANS: AApply the sum and difference of angles formulas to determine if the equations are identities.

FeedbackA Correct!B Did you apply the sum and difference of angles formulas correctly in the second

equation?C Did you apply the sum and difference of angles formulas correctly in the first equation?D Did you apply the sum and difference of angles formula correctly in both the equations?


35. ANS: DApply the sum and difference of angles formulas to determine if the equations are identities.

FeedbackA Did you apply the sum and difference of angles formula correctly in both the equations?B Did you apply the sum and difference of angles formula correctly in the second

equation?C Did you apply the sum and difference of angles formulas correctly in the first equation?D Correct!



FeedbackA Did you apply the sum and difference of angles formula correctly in both the equations?B Did you apply the sum and difference of angles formula correctly in the first equation?C Did you apply the sum and difference of angles formula correctly in the second

equation?D Correct!

PTS: 1 DIF: Advanced REF: Page 789 OBJ: 14-5.2 Verify identities by using sum and difference formulas. TOP: Verify identities by using sum and difference formulas. KEY: Trigonometric Identities | Sum and Difference Formulas

ID: A

13


FeedbackA Did you apply the sum and difference of angles formula correctly in both the equations?B Did you apply the sum and difference of angles formula correctly in the first equation?C Did you apply the sum and difference of angles formulas correctly in the second

equation?D Correct!


38. ANS: AWrite the solution in terms of degrees.

FeedbackA Correct!B Did you check the sign of the equation?C Did you substitute the correct values in the equation?D Did you simplify the equation correctly?

PTS: 1 DIF: Average REF: Page 803 OBJ: 14-7.1 Solve trigonometric equations. TOP: Solve trigonometric equations.KEY: Trigonometric Equations

39. ANS: CWrite the appropriate function.

FeedbackA You have interchanged the values in the function.B Did you apply the correct trigonometric function?C Correct!D Did you perform the correct arithmetic operation?

PTS: 1 DIF: Advanced REF: Page 803 OBJ: 14-7.2 Use trigonometric equations to solve real-world problems. TOP: Use trigonometric equations to solve real-world problems. KEY: Trigonometric Equations | Real-World Problems

ID: A

14

40. ANS: ASubstitute the values in the given equation and plot the graph.

FeedbackA Correct!B The period is incorrect.C You have plotted the incorrect amplitude.D Did you substitute the values in the equation correctly?

PTS: 1 DIF: Basic REF: Page 803 OBJ: 14-7.2 Use trigonometric equations to solve real-world problems. TOP: Use trigonometric equations to solve real-world problems. KEY: Trigonometric Equations | Real-World Problems

41. ANS: CNotice the curve along the x-axis and y-axis.

FeedbackA Did you interpret the graph correctly?B Did you count from the beginning of the curve?C Correct!D Did you count for the first 10 seconds?


42. ANS: AWrite the appropriate function.

FeedbackA Correct!B Did you use the correct trigonometric function?C The values in the function are interchanged.D Did you perform the correct arithmetic operation?


ID: A

15

43. ANS: DExpress S as a function of θ. Substitute the values in the function to determine the value of θ.

FeedbackA Check the sign of the answer.B Did you substitute the correct values?C The values in the function are interchanged.D Correct!


44. ANS: DWrite the appropriate function.

FeedbackA Did you perform the correct arithmetic operation?B Did you use the correct trigonometric function?C You have interchanged the values in the function.D Correct!


45. ANS: DSubstitute the values in the given equation and plot the graph.

FeedbackA The value of the amplitude in the equation is incorrect.B The period in the equation is incorrect.C The period plotted on the graph is incorrect.D Correct!


ID: A

16

46. ANS: CNotice the curve along the x-axis and y-axis.

FeedbackA Did you interpret the graph correctly?B Did you count from the beginning of the curve?C Correct!D Did you count for the first 10 seconds?


ID: A

17

47. ANS: x + x − y + x + y = 180°3x = 180°∴ x = 60°x = 4y60° = 4yy = 15°x − y + a = 180°60° − 15° + a = 180°a = 180° − 45°

a. a = 135°b. 60°, 45°, 75°c. a = 150°

Assessment RubricLevel 3 Superior*Shows thorough understanding of concepts.*Uses appropriate strategies.*Computation is correct.*Written explanation is exemplary.*Diagram/table/chart is accurate (as applicable).*Goes beyond requirements of problem.

Level 2 Satisfactory*Shows understanding of concepts.*Uses appropriate strategies.*Computation is mostly correct.*Written explanation is effective.*Diagram/table/chart is mostly accurate (as applicable).*Satisfies all requirements of problem.

Level 1 Nearly Satisfactory*Shows understanding of most concepts.*May not use appropriate strategies.*Computation is mostly correct.*Written explanation is satisfactory.*Diagram/table/chart is mostly accurate (as applicable).*Satisfies most of the requirements of problem.

Level 0 Unsatisfactory*Shows little or no understanding of the concept.*May not use appropriate strategies.*Computation is incorrect.*Written explanation is not satisfactory.*Diagram/table/chart is not accurate (as applicable).*Does not satisfy requirements of problem.

PTS: 1 DIF: Average REF: Page 759 OBJ: 13-8.1 Solve problems and show solutions. TOP: Solve problems and show solutions.

ID: A

18

KEY: Problem Solving | Show Solutions 48. ANS:

a. d = 4b. b = 3c. a = 9





PTS: 1 DIF: Average REF: Page 759 OBJ: 13-8.1 Solve problems and show solutions. TOP: Solve problems and show solutions.KEY: Problem Solving | Show Solutions

ID: A

19

49. ANS: Substitute m with the values ranging from 1 to 6.3(1) + 1 = 43(2) + 1 = 73(3) + 1 = 103(4) + 1 = 133(5) + 1 = 163(6) + 1 = 19a. The lowest value is 7.b. The maximum value is 19.





PTS: 1 DIF: Advanced REF: Page 811 OBJ: 14-8.1 Solve problems and show solutions. TOP: Solve problems and show solutions.KEY: Problem Solving | Show Solutions

ID: A

20

50. ANS:

Multiply the second equation by 14.

b = 14 c

Divide both sides by c.bc = 1

4Arrange the first equation in the following manner:3a = 7bMultiply the second equation by 3.3c = 12b Divide the first equation by the second equation.ac=

712

a. The ratio of b to c is 14

.

b. The ratio of a to c is 712

.




Level 0 Unsatisfactory*Shows little or no understanding of the concept.*May not use appropriate strategies.*Computation is incorrect.

ID: A

21

*Written explanation is not satisfactory.*Diagram/table/chart is not accurate (as applicable).*Does not satisfy requirements of problem.

PTS: 1 DIF: Advanced REF: Page 811 OBJ: 14-8.1 Solve problems and show solutions. TOP: Solve problems and show solutions.KEY: Problem Solving | Show Solutions

review chapters 13-14€¦ · b. ∠p =10°, q ≈2.6, p ≈15.2 d ... a 15-m long ladder rests...

Documents