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_________________________________

I.D. Number

_______________________

Unit 5 Evaluation

Evaluation 05

Second Year Algebra 2

(MTHH 040 059)

This evaluation will cover the lessons in this unit. It is open book, meaning you can use your syllabus

and other course materials. You will need to understand, analyze, and apply the information you

have learned in order to answer the questions correctly. To submit the evaluation by mail, follow the

directions on your Enrollment Information Sheet. To take the evaluation online, access the online

version of your course; use the navigation panel to access the prep page for this evaluation and

follow the directions provided. Note: A graphing calculator may be used on unit evaluations. You

may also use scratch paper to work out the solutions.

Multiple-Choice

Select the response that best completes the statement or answers the question.

_____ 1. A periodic function goes through 5 complete cycles in 4 minutes. What is the period of the

function?

1

min

5

1

b.

min

4

a.

c. 48 s

d. 75 s

_____ 2. The period of a periodic function is 8 s. How many cycles does it go through in 30 s?

a.

4

15

b. 3.75

c. 22

d. 240

_____ 3. Which of the following is not the graph of a periodic function?

a. I

b. II

c. III

d. both II and III

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_____ 4. The amplitude of a periodic function is 2.5 and its minimum value is 0. What is the

function’s maximum value?

a. −2.5

b. 0

c. 2.5

d. 5.0

_____ 5. Which angle in standard position is not coterminal with the others?

a. −190°

b. −170°

c. 190°

d. 550°

_____ 6. An angle drawn in standard position has a terminal side that passes through the point

( 2 , − 2 ). What is one possible measure of the angle?

a. 45°

b. 225°

c. 315°

d. 330°

_____ 7. An angle of 120° is in standard position. What are the coordinates of the point at which the

terminal side intersects the unit circle?

1 3

a. ,

2 2

1

3

b. ,

2

2

3 1

,

c.

2 2

1 3

d. ,

2 2

_____ 8. An angle of −225° is in standard position. Which points can lie on the terminal side of the

angle?

2

2

,

I.

2

2

2 2

,

II.

2 2

2

2

,

III.

2

2

IV. (−1, 1)

a. I and II

b. II and III

c. II and IV

d. I and III

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_____ 9. Which pairs of measurements represent the same angle measures?

7

radians

6

240°;

I.

II.

135°;

3

radians

4

III.

150°;

5

radians

6

a. I and II

b. I and III

c. II and III

d. I, II, and III

5

_____ 10. What is the exact value of cos

radians ?

4

a. −

3

2

2

2

1

c. −

2

2

d.

2

b. −

_____ 11. In a circle, an arc of length 8 cm is intercepted by a central angle of

2

radians. What

3

is the radius of the circle?

3

cm

16

16

b.

cm

3

a.

16 2

cm

3

d. 12 cm

c.

_____ 12. Two arcs have the same length. One arc is intercepted by an angle of

3

radians in a

2

circle of radius 15 cm. If the radius of the other circle is 25 cm, what central angle

intercepts the arc?

3

2

9

b.

10

7

c.

6

5

d.

3

a.

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radians

radians

radians

radians

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_____ 13. Which value is not the same as the other three values?

a. sin 100°

b. sin 80°

c. sin −80°

d. sin −260°

_____ 14. What is the amplitude of y = 3 sin 4θ?

a.

4

3

b. 3

c. 4

d. 2

_____ 15. Which answer choice describes y = −sin 2θ?

a. amplitude −1, period 4

b. amplitude 1, period

c. amplitude 2, period −

d. amplitude 2 , period 1

_____ 16. Which function has a period of 4 and an amplitude of 8?

a. y = −8 sin 8θ

b. y = −8 sin

1

θ

2

c. y = 8 sin 2θ

d. y = 4 sin 8θ

_____ 17. Which of the following statement(s) is (are) true?

cos (θ) = cos (−θ)

I.

II.

cos (θ + 2 ) = cos (θ)

III.

cos

= − cos

a. I and II

b. II

c. I and III

d. I, II, and III

_____ 18. Which function has a period of 2 and an amplitude of 4?

a. f(x) = 2 cos 4θ

b. f(x) = 2 cos θ

c. f(x) = 4 cos 2θ

d. f(x) = 4 cos θ

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_____ 19. Which equation corresponds to the graph shown? The screen dimensions are

−4 ≤ x ≤ 4 and −2 ≤ y ≤ 2.

1

x

cos

2

4

1

b. y = cos 4x

2

x

c. y = 2 cos

4

a. y =

d. y = 2 cos 4x

_____ 20. Which equation has the same graph as y = − cos t ?

a. y = cos (−t)

b. y = sin (t – )

c. y = cos (t – )

d. y = − sin t

_____ 21. Which of the following values is not defined?

a. tan 0

b. tan

c. tan

1

d.

tan

3

2

4

_____ 22. What is the exact value of tan

7

?

6

a. − 3

b.

3

3

c.

3

3

d.

3

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_____ 23. Which equation does not represent a vertical asymptote of the graph of y = tan θ?

a. θ = −

2

b. θ = 0

c. θ =

2

3

d. θ =

2

_____ 24. Which function has a period of 4 ?

a. y = tan 4θ

b. y = tan 2θ

1

θ

2

1

d. y = tan θ

4

c. y = tan

_____ 25. Which function is a phase shift of y = sin θ by 5 units to the left?

a. y = 5 sin θ

b. y = sin θ + 5

c. y = sin (θ + 5)

d. y = sin 5θ

_____ 26. Which function is a translation of y = cos θ by 5 units down?

a. y = −5 cos θ

b. y = cos θ – 5

c. y = cos (θ – 5)

d. y = cos (−5θ)

_____ 27. Which function is a translation of y = sin θ that is

a. y = sin (θ +

b. y = sin (θ +

c. y = sin (θ –

d. y = sin (θ –

Unit 5 Evaluation

3

2

2

3

)+

)+

)+

)–

3

units up and

2

units to the left?

2

3

3

2

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_____ 28. Suppose cos 45°. Find the exact value of sec θ.

2

a.

2

2

1

c.

2

3

d.

4

b.

_____ 29. Suppose tan (−30°). Find the exact value of cot θ.

3

a.

b. − 3

3

3

c.

d. −

3

3

_____ 30. Find csc 70°.

a. 0.3420

b. 0.9397

c. 1.0642

d. 2.9238

_____ 31. Write the measure of 270 in radians.

2

5

3

b.

2

a.

c.

d.

2

_____ 32. Write the measure of −3 radians in degrees.

a. −540

b. −360

c. −300

d. −60

_____ 33. The ____________ of a function is the length of one cycle.

a. amplitude

b. unit circle

c. period

d. phase shift

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_____ 34. A horizontal translation of a periodic function is a ____________.

a. sine function

b. cosine function

c. unit circle

d. phase shift

_____ 35. Which sketch in standard position represents −315?

a.

b.

c.

d.

_____ 36. Which sketch in standard position represents 240?

a.

b.

c.

d.

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_____ 37. Which sketch in standard position represents −340?

a.

b.

c.

d.

_____ 38. Which graph represents the function y = 2 cos x?

a.

b.

c.

d.

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_____ 39. Which graph represents the function y = 3 sin 2x?

a.

b.

c.

d.

_____ 40. Which graph represents the function y = −sin 3x?

a.

b.

c.

d.

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_____ 41. Which graph represents the function y = cos 4x?

a.

b.

c.

d.

_____ 42. Which graph represents the function y = −3 cos(x +

a.

b.

c.

d.

Unit 5 Evaluation

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) + 3?

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_____ 43. Which graph represents the function y = 2 sin (2x –

a.

b.

c.

d.

_____ 44. Which graph represents the function y = −sin (x –

a.

b.

c.

d.

Unit 5 Evaluation

330

4

3

) – 2?

) + 1?

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_____ 45. Which graph represents the function y = 3 cos(3x +

a.

b.

c.

d.

2

) – 1?

_____ 46. Identify the amplitude and period of the function, y = 2 cos

x

.

4

a. 2, 8

b. 2, 4

c. 4, 2

d. 2,

8

_____ 47. Identify the amplitude and period of the function, y =

a. 9,

1

sin 5x.

9

2

5

1

, 5

9

1 2

c. ,

9 5

b.

d. 5,

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331

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_____ 48. Write the measure of 5 radians in degrees.

a. 900

b. 180

c. 36

d. 450

_____ 49. Write the measure of −45 in radians.

a.

4

b. 45

c. −

d. −

2

4

_____ 50. Find the period and amplitude of this graph.

a. 4, 1.5

b. 4, 2

c. 1, 2.5

d. 2, 2

Carefully check your answers on this evaluation and make any corrections you feel are

necessary. When you are satisfied that you have answered the questions to the best of your

ability, transfer your answers to an answer sheet. Please refer to the information sheet that

came with your course materials.

Unit 5 Evaluation

332

MTHH 040