Test 3 Trig Functions - WordPress.com · 2016-11-24 · Test 3 Trig Functions Multiple Choice ......

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

1

Test 3 Trig Functions

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

____ 1. What is the value of sec 70 to the nearest thousandth?

A. 0.342 C. –2.924B. 0.364 D. 2.924

____ 2. What is the value of cos 295( ) to the nearest thousandth?

A. 2.364 C. 0.423B. –0.423 D. 2.145

____ 3. What is the value of cos 453 to the nearest thousandth?

A. –19.081 C. 0.052B. –0.052 D. –19.231

____ 4. What is the measure of the reference angle for an angle of 310 in standard position?

A. 310º C. 50ºB. –50º D. –130º

____ 5. Which of these angles is coterminal with an angle of 230 in standard position?

A. –130º C. –230ºB. 130º D. 40º

____ 6. Which of these angles is NOT coterminal with an angle of 240 in standard position?

A. 120º C. –60ºB. –600º D. 480º

____ 7. Which expression represents the measures of all the angles coterminal with 301 in standard position?

A. 301 k180, k Z C. 301 k360, k òB. 59 k360, k Z D. 301 k360, k Z

Name: ________________________ ID: A

2

____ 8. Given tan 89

, which statement is true for all possible values of ?

A. cot 98

B. cot 98

C. cot 89

D. cot cannot be determined

____ 9. What is the length of the arc that subtends a central angle of 150 in the unit circle?

A.56 units C.

65 units

B. 75 units D.512 units

____ 10. In the unit circle, the length of the arc that subtends a positive central angle of is 13 units.

What is the measure of in degrees?

A. 120 C.1

540

B. 60 D. 60

____ 11. In a circle with radius 8 units, the length of the arc that subtends a positive central angle of is 209 units. What is the measure of in degrees?

A. 100 C. 50B. 50 D. 400

____ 12. What is 85 in radians?

A. 85 radians C.1736

radians

B.15 300 radians D.

1736 radians


A. –240 radians C.43 200

radians

B. 43

radians D. 43 radians

Name: ________________________ ID: A

3


A.13936

radians C. 695 radians

B.125 100

radians D.13936

radians

____ 15. What is –6 radians in degrees?

A. –344 C. –1080B. –19 D. –2

____ 16. What is the value of sec 47

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃ to the nearest hundredth?

A. 1.19 C. –0.22B. 1.00 D. –4.49

____ 17. What is the value of csc 3.7( ) to the nearest hundredth?

A. 1.89 C. 1.24B. –15.50 D. 0.53

____ 18. In a circle with radius 5 cm, what is the length of the arc that subtends a central angle of 3

4 radians? Give the answer to the nearest tenth.

A. 11.8 cm C. 3.8 cmB. 0.5 cm D. 2.4 cm

____ 19. Which angle is NOT coterminal with an angle of 25 radians in standard position?

A. 125 C. 0

B.85 D.

185

Name: ________________________ ID: A

4

____ 20. Which function below has this graph?

A. y sin xB. y tan xC. y cos xD. None of the above

____ 21. Which function below has this graph?

A. y sec xB. y csc xC. y cotxD. None of the above

Name: ________________________ ID: A

5

____ 22. Which set of functions describes these graphs?

A. y cos xy 2cos xy 4cos x

B. y cos xy cos 2xy cos 4x

C. y cos x

y cos x 2

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃

y cos x 4

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃

D. y cos xy cos x 2y cos x 4

____ 23. What is the amplitude of the function y 9sin x?

A. 9 C. 9B. 18 D. –9

____ 24. What is the amplitude of this sinusoidal function?

A. 3 C. 6B. 2 D. –3

Name: ________________________ ID: A

6

____ 25. What is the period of the function y tan 5x?

A.5

C.25

B.5 D.

5

____ 26. What is the period of this function?

y f(x)

A.2

C.2

B.4

D.2

____ 27. What is the phase shift of the function y cos x 56

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃ ?

A.56

C.76

B.17

6D.

56

____ 28. This graph is the image of y cos x after a phase shift.Which value below could represent the phase shift?

A.13

6C.

6

B.11

6D.

6

Name: ________________________ ID: A

7

____ 29. Which function below describes this graph?

A. y sin x 3( ) C. y sin xB. y sin x 3 D. y 3sin x

____ 30. Which function below describes this graph?

A. y sin x C. y sin x 2B. y sin 2x D. y 2sin x

____ 31. Which number is NOT in the domain of y tan 3x?

A. 76 C. 4

3

B. D. 13

Name: ________________________ ID: A

8

____ 32. Identify the transformations that would be applied to the graph of y sin x to get the graph of

y sin12

xÊ

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃ 1.

A. A vertical stretch by a factor of 2, and then a translation of 1 unit down

B. A horizontal compression by a factor of 12

, and then a translation of 1 unit down

C. A horizontal stretch by a factor of 2, and then a translation of 1 unit down

D. A horizontal stretch by a factor of 1, and then a translation of 12

units right

____ 33. What is the amplitude of the graph of y 8sin 2 x 25

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃ 9?

A. 16 C. –1B. 2 D. 8

____ 34. What is the equation of the centre line of the graph of the function y 2cos 5 x 56

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃ 6?

A. y –6 C. y –12

B. y –4 D. y 56

____ 35. What is the period of the function y 2sin 3 x 57

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃ 8?

A.23

C.57

B.75

D.32

____ 36. What is the range of the function y 2cos 3 x 5

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃ 5?

A. 7 y 3 C. 2 y 8B. 3 y 7 D. 3 y 7

Name: ________________________ ID: A

9

____ 37. Which function below best describes this graph?

A. y sin3 x 2( ) 5 C. y sin

3 x 2( ) 5

B. y sin3

x 2( ) 5 D. y sin3

x 2( ) 5

____ 38. Suppose the function y 19cos29

x 4.5( ) 23 models the height, y metres, of a seat on a Ferris wheel at

any time x minutes after the wheel begins to rotate. What is the diameter of the wheel?

A. 19 m C. 38 mB. 9 m D. 42 m

____ 39. Which of the following angles, in degrees, is coterminal with, but not equal to, 15 radians?

A. 36° C. 306°B. 216° D. 396°

____ 40. Determine the equation of a circle with centre at the origin and radius 8.

A. x 2 y 2 8 C. x 2 y 2 16

B. x 2 y 2 64 D. x 2 y 2 8

Name: ________________________ ID: A

10

____ 41. Which graph represents an angle in standard position with a measure of 285°?A. C.

B. D.

____ 42. Determine the measure of the angle in standard position shown on the graph below. Round your answer to the nearest tenth of a degree.

A. 291.8° C. 111.8°B. 201.8° D. 21.8°

Name: ________________________ ID: A

11

____ 43. The coordinates of the point that lies at the intersection of the terminal arm and the unit circle at an angle of 33° areA. (0.84, 0.65) C. (0.84, 0.54)B. (0.65, 0.54) D. (0.54, 0.84)

____ 44. Identify the point on the unit circle corresponding to an angle of 6

radians in standard position.

A. (3

2,

12

) C. (3

2,

33

)

B. (12

, 3

2) D. (

33

, 12

)

____ 45. Which point on the unit circle corresponds to tan = 0?A. (1,1) C. (0,0)B. (0,1) D. (1,0)

____ 46. If the angle is 1400° in standard position, it can be described as having made

A. 389

rotations C. 389

rotations

B. 779

rotations D. 779

rotations

Name: ________________________ ID: A

12

____ 47. Which graph represents the function y = 2cos(53

x), where x is in degrees?

A. C.

B. D.

____ 48. The graph of y sin x can be obtained by translating the graph of y cos x

A.4

units to the right C. units to the right

B.3

units to the right D.2

units to the right

____ 49. Give an equation for a transformed sine function with an amplitude of 97

, a period of 12

, a phase shift of 78

rad

to the right, and a vertical translation of 3 units down.

A. y = 97

sin 4 x 7 / 8( ) – 3 C. y = 97

sin 4 x 7 / 8( )ÈÎÍÍÍ

˘˚˙̇̇ 3

B. y = 97

sin 4 x 7 / 8( )ÈÎÍÍÍ

˘˚˙̇̇ 3 D. y =

97

sin 4 x 7 / 8( ) – 3

____ 50. Which of the following is not an asymptote of the function f ( ) tan?

A. x C. x = 92

B. x = 72 D. x =

32

Name: ________________________ ID: A

13

Short Answer

1. Sketch the angle –40° in standard position, then identify the reference angle.

2. Determine the exact value of sin(120).

3. Determine the exact value of csc 405.

4. For the point P(2,4) on the terminal arm of an angle in standard position, determine the exact value of cot .

5. Sketch the angle 12 radians in standard position.

6. The graph of y sin x is shown below for 0 x 2.Extend the graph for x 2 and for x 0.

Name: ________________________ ID: A

14

7. The graph of y cos x is shown below.On the same grid, sketch the graph of y 4cos x .

8. The graph of y cos x is shown below.On the same grid, sketch the graph of y cos 2x .

y cos x

9. The graph of y cos x is shown below.On the same grid, sketch the graph of y cos x 2.

y cos x

Name: ________________________ ID: A

15

10. The graph of y sin x is shown below.

On the same grid, sketch the graph of y sin x 6

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃ .

y sin x

11. Write a general equation for the asymptotes of the graph of y tan 4x( ) .

12. Identify the following characteristics of the graph of y 3cos 2 x 2

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃ shown below.

• amplitude• period• equation of the centre line

• phase shift• zeros• domain

• minimum value• maximum value• range

y 3cos 2 x 2

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃

13. Write an equation for a sine function with amplitude 8, period 23

, equation of centre line y 9, and phase

shift 4

.

Name: ________________________ ID: A

16

14. Write an equation that represents the sine function graphed below.

15. A table fan has a mark on the tip of one blade. The equation y 17cos 6x( ) 28 represents the height of the mark, y centimetres, above the table x seconds after the fan is turned on. What is the height of the mark above the table when it is closest to the table?

16. Find the exact value of cos56

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃

È

Î

ÍÍÍÍÍÍÍÍÍ

˘

˚

˙̇̇˙̇̇˙̇̇

2

sin56

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃

È

Î

ÍÍÍÍÍÍÍÍÍ

˘

˚

˙̇̇˙̇̇˙̇̇

2

.

Problem

1. P(3,5) is a terminal point of angle in standard position. Determine all possible measures of in the domain 740 20. Give the answers to the nearest degree.

2. Given cot 1, determine all possible measures of angle in the domain 2 2 .

Name: ________________________ ID: A

17

3. Graph y 2sin x . Identify the amplitude, period, general expression for the zeros, domain of the function, and range of the function.

4. Graph y sin 4x . Identify the amplitude, period, general expression for the zeros, general equation for the asymptotes, domain of the function, and range of the function.

Name: ________________________ ID: A

18

5. The graph of y sin x is shown below. On the same grid, sketch the graph of y 4sin 2 x 4

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃ 1.

Describe these characteristics of this function: amplitude, period, phase shift, equation of the centre line, domain, and range

y sin x

6. Sketch the graph of y 4sin 4x 23

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃ 2.

Describe these characteristics of the function: amplitude, period, phase shift, equation of the centre line, domain, and range

ID: A

1

Test 3 Trig FunctionsAnswer Section

MULTIPLE CHOICE

1. ANS: D PTS: 1 DIF: Easy REF: 6.1 Trigonometric Ratios for Any Angle in Standard Position LOC: 12.T3 TOP: Trigonometry KEY: Procedural Knowledge

2. ANS: C PTS: 1 DIF: Easy REF: 6.1 Trigonometric Ratios for Any Angle in Standard Position LOC: 12.T3 TOP: Trigonometry KEY: Procedural Knowledge

3. ANS: B PTS: 1 DIF: Easy REF: 6.1 Trigonometric Ratios for Any Angle in Standard Position LOC: 12.T3 TOP: Trigonometry KEY: Procedural Knowledge

4. ANS: C PTS: 1 DIF: Easy REF: 6.1 Trigonometric Ratios for Any Angle in Standard Position LOC: 12.T1 TOP: Trigonometry KEY: Conceptual Understanding | Procedural Knowledge

5. ANS: A PTS: 1 DIF: Easy REF: 6.1 Trigonometric Ratios for Any Angle in Standard Position LOC: 12.T1 TOP: Trigonometry KEY: Conceptual Understanding | Procedural Knowledge

6. ANS: C PTS: 1 DIF: Easy REF: 6.1 Trigonometric Ratios for Any Angle in Standard Position LOC: 12.T1 TOP: Trigonometry KEY: Conceptual Understanding | Procedural Knowledge

7. ANS: D PTS: 1 DIF: Easy REF: 6.1 Trigonometric Ratios for Any Angle in Standard Position LOC: 12.T1 TOP: Trigonometry KEY: Conceptual Understanding

8. ANS: A PTS: 1 DIF: Easy REF: 6.1 Trigonometric Ratios for Any Angle in Standard Position LOC: 12.T3 TOP: Trigonometry KEY: Conceptual Understanding

9. ANS: A PTS: 1 DIF: Easy REF: 6.2 Angles in Standard Position and Arc Length LOC: 12.T1TOP: Trigonometry KEY: Procedural Knowledge | Conceptual Understanding

10. ANS: D PTS: 1 DIF: Moderate REF: 6.2 Angles in Standard Position and Arc Length LOC: 12.T1TOP: Trigonometry KEY: Procedural Knowledge | Conceptual Understanding | Problem-Solving Skills

11. ANS: C PTS: 1 DIF: Moderate REF: 6.2 Angles in Standard Position and Arc Length LOC: 12.T1TOP: Trigonometry KEY: Procedural Knowledge | Conceptual Understanding | Problem-Solving Skills

12. ANS: D PTS: 1 DIF: Easy REF: 6.3 Radian MeasureLOC: 12.T1 TOP: Trigonometry KEY: Procedural Knowledge


ID: A

2

14. ANS: A PTS: 1 DIF: Easy REF: 6.3 Radian MeasureLOC: 12.T1 TOP: Trigonometry KEY: Procedural Knowledge

15. ANS: C PTS: 1 DIF: Easy REF: 6.3 Radian MeasureLOC: 12.T1 TOP: Trigonometry KEY: Procedural Knowledge


17. ANS: A PTS: 1 DIF: Easy REF: 6.3 Radian MeasureLOC: 12.T3 TOP: Trigonometry KEY: Procedural Knowledge

18. ANS: A PTS: 1 DIF: Easy REF: 6.3 Radian MeasureLOC: 12.T1 TOP: Trigonometry KEY: Procedural Knowledge | Conceptual Understanding

19. ANS: C PTS: 1 DIF: Moderate REF: 6.3 Radian MeasureLOC: 12.T1 TOP: Trigonometry KEY: Conceptual Understanding | Procedural Knowledge

20. ANS: B PTS: 1 DIF: Easy REF: 6.4 Graphing Trigonometric Functions LOC: 12.T4TOP: Trigonometry KEY: Conceptual Understanding

21. ANS: A PTS: 1 DIF: Difficult REF: 6.4 Graphing Trigonometric Functions LOC: 12.T4TOP: Trigonometry KEY: Conceptual Understanding | Problem-Solving Skills

22. ANS: A PTS: 1 DIF: Easy REF: 6.5 Trigonometric FunctionsLOC: 12.T4 TOP: Trigonometry KEY: Conceptual Understanding

23. ANS: C PTS: 1 DIF: Easy REF: 6.5 Trigonometric FunctionsLOC: 12.T4 TOP: Trigonometry KEY: Procedural Knowledge | Conceptual Understanding

24. ANS: A PTS: 1 DIF: Easy REF: 6.5 Trigonometric FunctionsLOC: 12.T4 TOP: Trigonometry KEY: Procedural Knowledge | Conceptual Understanding

25. ANS: D PTS: 1 DIF: Easy REF: 6.5 Trigonometric FunctionsLOC: 12.T4 TOP: Trigonometry KEY: Procedural Knowledge

26. ANS: A PTS: 1 DIF: Moderate REF: 6.5 Trigonometric FunctionsLOC: 12.T4 TOP: Trigonometry KEY: Procedural Knowledge

27. ANS: A PTS: 1 DIF: Easy REF: 6.5 Trigonometric FunctionsLOC: 12.T4 TOP: Trigonometry KEY: Procedural Knowledge

28. ANS: D PTS: 1 DIF: Moderate REF: 6.5 Trigonometric FunctionsLOC: 12.T4 TOP: Trigonometry KEY: Conceptual Understanding | Procedural Knowledge

29. ANS: D PTS: 1 DIF: Easy REF: 6.5 Trigonometric FunctionsLOC: 12.T4 TOP: Trigonometry KEY: Conceptual Understanding

30. ANS: B PTS: 1 DIF: Moderate REF: 6.5 Trigonometric FunctionsLOC: 12.T4 TOP: Trigonometry KEY: Conceptual Understanding

31. ANS: A PTS: 1 DIF: Moderate REF: 6.5 Trigonometric FunctionsLOC: 12.T4 TOP: Trigonometry KEY: Conceptual Understanding | Procedural Knowledge

32. ANS: C PTS: 1 DIF: Easy REF: 6.6 Combining Transformations of Sinusoidal Functions LOC: 12.T4TOP: Trigonometry KEY: Procedural Knowledge

ID: A

3

33. ANS: D PTS: 1 DIF: Easy REF: 6.6 Combining Transformations of Sinusoidal Functions LOC: 12.T4TOP: Trigonometry KEY: Procedural Knowledge

34. ANS: A PTS: 1 DIF: Easy REF: 6.6 Combining Transformations of Sinusoidal Functions LOC: 12.T4TOP: Trigonometry KEY: Procedural Knowledge

35. ANS: A PTS: 1 DIF: Moderate REF: 6.6 Combining Transformations of Sinusoidal Functions LOC: 12.T4TOP: Trigonometry KEY: Procedural Knowledge

36. ANS: D PTS: 1 DIF: Moderate REF: 6.6 Combining Transformations of Sinusoidal Functions LOC: 12.T4TOP: Trigonometry KEY: Procedural Knowledge | Conceptual Understanding

37. ANS: D PTS: 1 DIF: Moderate REF: 6.7 Applications of Sinusoidal Functions LOC: 12.T4TOP: Trigonometry KEY: Procedural Knowledge | Conceptual Understanding

38. ANS: C PTS: 1 DIF: Moderate REF: 6.7 Applications of Sinusoidal Functions LOC: 12.T4TOP: Trigonometry KEY: Procedural Knowledge | Conceptual Understanding

39. ANS: D PTS: 1 DIF: Average OBJ: Section 4.1NAT: T1 TOP: Angles and Angle Measure KEY: radians | degrees

40. ANS: B PTS: 1 DIF: Easy OBJ: Section 4.2NAT: T2 TOP: Unit Circle KEY: unit circle | unit circle equation

41. ANS: C PTS: 1 DIF: Easy OBJ: Section 4.1NAT: T1 TOP: Angles and Angle Measure KEY: degrees

42. ANS: D PTS: 1 DIF: Easy OBJ: Section 4.1NAT: T1 TOP: Angles and Angle Measure KEY: radians

43. ANS: C PTS: 1 DIF: Average OBJ: Section 4.3NAT: T2 TOP: Trigonometric Ratios KEY: trigonometric ratios | unit circle | terminal arm | angle

44. ANS: A PTS: 1 DIF: Average OBJ: Section 4.3NAT: T2 TOP: Trigonometric Ratios KEY: exact value | unit circle | radiansNOT: tan90 and tan270 do not include undefined

45. ANS: D PTS: 1 DIF: Average OBJ: Section 4.3NAT: T2 TOP: Trigonometric Ratios KEY: Unit Circle | exact value | tangent ratio

46. ANS: C PTS: 1 DIF: Average OBJ: Section 4.1NAT: T1 TOP: Angles and Angle Measure KEY: rotations | standard positionNOT: Mixed numbers

47. ANS: B PTS: 1 DIF: Difficult OBJ: Section 5.1NAT: T4 TOP: Graphing Sine and Cosine Functions KEY: graph | amplitude | period | sinusoidal function

48. ANS: D PTS: 1 DIF: Easy OBJ: Section 5.2NAT: T4 TOP: Transformations of Sinusoidal Functions KEY: translation | primary trigonometric function

49. ANS: A PTS: 1 DIF: Difficult OBJ: Section 5.2NAT: T4 TOP: Transformations of Sinusoidal Functions KEY: transformations | equation | properties | sinusoidal function

ID: A

4

50. ANS: A PTS: 1 DIF: Easy OBJ: Section 5.3NAT: T4 TOP: The Tangent Function KEY: asymptote | tangent function

SHORT ANSWER

1. ANS:

Reference angle: 40°

PTS: 1 DIF: Easy REF: 6.1 Trigonometric Ratios for Any Angle in Standard Position LOC: 12.T1 TOP: Trigonometry KEY: Procedural Knowledge | Conceptual Understanding | Communication

2. ANS:

sin 120( ) 3

2

PTS: 1 DIF: Moderate REF: 6.1 Trigonometric Ratios for Any Angle in Standard Position LOC: 12.T3 TOP: Trigonometry KEY: Procedural Knowledge | Conceptual Understanding

3. ANS:

csc 405 2


4. ANS:

cot 12


ID: A

5

5. ANS:

PTS: 1 DIF: Easy REF: 6.3 Radian Measure LOC: 12.T1 TOP: Trigonometry KEY: Procedural Knowledge | Conceptual Understanding | Communication

6. ANS:

PTS: 1 DIF: Easy REF: 6.4 Graphing Trigonometric FunctionsLOC: 12.T4 TOP: Trigonometry KEY: Procedural Knowledge

7. ANS:

PTS: 1 DIF: Easy REF: 6.5 Trigonometric FunctionsLOC: 12.T4 TOP: Trigonometry KEY: Procedural Knowledge | Communication

ID: A

6

8. ANS: y cos 2x

y cos x


9. ANS:

y cos x

y cos x 2


ID: A

7

10. ANS:

y sin x 6

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃

y sin x

PTS: 1 DIF: Moderate REF: 6.5 Trigonometric FunctionsLOC: 12.T4 TOP: Trigonometry KEY: Procedural Knowledge | Communication

11. ANS: Equations may vary. For example:

x 2k 1( )8

, k Z

PTS: 1 DIF: Moderate REF: 6.5 Trigonometric FunctionsLOC: 12.T4 TOP: Trigonometry KEY: Conceptual Understanding | Procedural Knowledge

12. ANS: • amplitude: 3• period: • equation of the centre line: y 0

• phase shift: 2

• zeros: 74

, 54

, 34

, 4

,4

,34

,54

,74

• domain: 2 x 2• minimum value: –3• maximum value: 3• range: 3 y 3

PTS: 1 DIF: Easy REF: 6.6 Combining Transformations of Sinusoidal FunctionsLOC: 12.T4 TOP: Trigonometry KEY: Procedural Knowledge

13. ANS:

y 8sin 3 x 4

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃+9

PTS: 1 DIF: Easy REF: 6.6 Combining Transformations of Sinusoidal FunctionsLOC: 12.T4 TOP: Trigonometry KEY: Conceptual Understanding | Procedural Knowledge

ID: A

8

14. ANS: Students’ answers may vary. For example:

y 2sin25

x 1( ) 2.

PTS: 1 DIF: Moderate REF: 6.7 Applications of Sinusoidal FunctionsLOC: 12.T4 TOP: Trigonometry KEY: Conceptual Understanding | Procedural Knowledge

15. ANS: 11 cm

PTS: 1 DIF: Moderate REF: 6.7 Applications of Sinusoidal FunctionsLOC: 12.T4 TOP: Trigonometry KEY: Conceptual Understanding | Procedural Knowledge

16. ANS:

cos56

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃

È

Î

ÍÍÍÍÍÍÍÍÍ

˘

˚

˙̇̇˙̇̇˙̇̇

2

sin56

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃

È

Î

ÍÍÍÍÍÍÍÍÍ

˘

˚

˙̇̇˙̇̇˙̇̇

2

3

2

Ê

Ë

ÁÁÁÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃˜̃̃

2

12

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃

2

34 1

4

12

PTS: 1 DIF: Difficult OBJ: Section 4.3 NAT: T3TOP: Trigonometric Ratios KEY: exact value | unit circle

ID: A

9

PROBLEM

1. ANS: The terminal arm of angle lies in Quadrant 1.

The reference angle is: tan1 53

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃ Ö 59

In Quadrant 1, Ö 59

Sketch a diagram.

The angles that are coterminal with 59 in the domain 740 20 are approximately:59 360 301301 360 661

Possible values of are approximately: 661 and 301.

PTS: 1 DIF: Moderate REF: 6.1 Trigonometric Ratios for Any Angle in Standard Position LOC: 12.T3 TOP: Trigonometry KEY: Conceptual Understanding | Procedural Knowledge

ID: A

10

2. ANS: tan 1Since tan is negative, the terminal arm of angle lies in Quadrant 2 or Quadrant 4.

The reference angle is: tan1 (1) 4

In Quadrant 2: 4

, or 34

In Quadrant 4: 2 4

, or 74

Sketch a diagram.

An angle that is coterminal with 34

in the domain 2 2 is:

34

2 54

An angle that is coterminal with 74

in the domain 2 2 is:

74

2 4

So, the possible measures of angle are 34

, 5

4,

74

, and 4

PTS: 1 DIF: Moderate REF: 6.3 Radian Measure LOC: 12.T3 TOP: Trigonometry KEY: Procedural Knowledge | Conceptual Understanding

ID: A

11

3. ANS: The graph of y 2sin x is the image after the graph of y sin x has been stretched vertically by a factor of 2.

The amplitude is 2.The period is 2.The zeros are k , k Z.The domain is x ò.The range is 2 y 2.

PTS: 1 DIF: Moderate REF: 6.5 Trigonometric FunctionsLOC: 12.T4 TOP: Trigonometry KEY: Conceptual Understanding | Procedural Knowledge | Communication

ID: A

12

4. ANS: The graph of y sin 4x is the image after the graph of y sin x has been

horizontally compressed by a factor of 14

.

y sin 4x

The amplitude is 1.

The period is 12.

The zeros are k4

, k Z.

There are no asymptotes.The domain is x ò.The range is 1 y 1.

PTS: 1 DIF: Moderate REF: 6.5 Trigonometric FunctionsLOC: 12.T4 TOP: Trigonometry KEY: Conceptual Understanding | Procedural Knowledge | Communication

ID: A

13

5. ANS:

Compare y 4sin 2 x 4

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃ 1 to y a sin b x c( ) d :

a 4, so the graph of y sin x is stretched vertically by a factor of 4, and the amplitude is 4.

b 2, so the graph is compressed horizontally by a factor of 12

, and the period is 22

, or .

c 4

, so the graph is translated 4

units left, and the phase shift is 4

.

d 1, so the graph is translated 1 unit up, and the centre line has equation: y 1The domain is: x òThe maximum value of the function is: 1 4 5The minimum value of the function is: 1 4 3So, the range is: 3 y 5

y 4sin 2 x 4

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃ 1

y sin x

PTS: 1 DIF: Moderate REF: 6.6 Combining Transformations of Sinusoidal FunctionsLOC: 12.T4 TOP: Trigonometry KEY: Conceptual Understanding | Procedural Knowledge | Communication

ID: A

14

6. ANS:

Write y 4sin 4x 23

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃ 2 in the form y a sin b x c( ) d .

y 4sin 4 x 6

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃ 2

Compare to y a sin b x c( ) d :

a 4, b 4, c 6

, and d 2

The graph of y sin x is stretched vertically by a factor of 4, compressed horizontally by a factor of 14

,

reflected in the x-axis, and then translated 6

units left and 2 units up.

y 4sin 4x 23

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃ 2

a 4, so the amplitude is 4.

b 4, so the period is 24

, or 2

.

c 6

, so the phase shift is 6

.

d 2, so the equation of the centre line is y 2. The domain is x ò.The maximum y-value is 4 units above the centre line and the minimum y-value is 4 units below the centre line, so the range is 2 y 6.

PTS: 1 DIF: Difficult REF: 6.6 Combining Transformations of Sinusoidal FunctionsLOC: 12.T4 TOP: Trigonometry KEY: Conceptual Understanding | Procedural Knowledge | Communication

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