Algebra II B Review 5

Multiple Choice Identify the choice that best completes the statement or answers the question.

1. Find the measure of the angle below.

40ο

x

y

a. 135º b. 50º c. 310º d. 270º

Sketch the angle in standard position.

2. 140º

a.

140ο x

y c.

140ο

x

y

b.

140ο

x

y d.

140ο

x

y

3. Find the cosine and sine of 90º. Round your answers to the nearest hundredth if necessary.

90 ο

x

y

a. 0.71, 0.71 b. 0, 1 c. –0.71, 0.71 d. 1.1, 0

4. Find the exact value of cos 300º and sin 300º. a.

c.

b.

d.

Write the measure in radians. Express the answer in terms of π.

5. 140º

a. b. c.

d.

6. 45º a. b. c. d.

Write the measure in degrees.

7. radians

a. 300º b. º

c. 5.24º d. º

8. – radians

a. º

b. –144º c. –2.51º d. º

Use the graph of y = sin θ to find the value of sin θ for each value of θ.

9. 360º

a. 0.4 b. 0.2 c. 0 d. 0.6

10. 53 radians

a. –0.7 b. –0.3 c. –0.9 d. –0.5

11. Find the period of the graph shown below.

a. 2π b. 2

3 π c. 1

2 π d. π

12. Find the amplitude of the sine curve shown below.

a. 2π b. 1 c. 0.5 d. 2

13. Sketch one cycle of y = –3 sin 3θ. a. c.

b. d.

14. Write the equation for the sine function shown below.

a. c. b. d.

15. Find the period, range, and amplitude of the cosine function .

a.

b.

c.

d.

Write a cosine function for the graph.

16.

a. c.

b. d.

17. Use a graphing calculator to solve the equation in the interval from 0 to 2π. Round to the

nearest hundredth. a. 2.41, 4.17 c. 2.30, 3.98 b. 2.20, 4.09 d. –3.80, –2.20, 2.20, 3.80

18. Write an equation of the cosine function with amplitude 2 and period 4π. a.

c.

b.

d.

19. Use the graph of to find the value of y = tan 14 π. Round to the nearest tenth if necessary. If the

tangent is undefined at that point, write undefined.

a. 0.4 b. 1 c. 0 d. 2.4

20. Sketch the graph of the tangent curve y = tan 14 in the interval from 0 to 2π.

a. c.

b. d.

21. Use a graphing calculator to graph the function on the interval and .

Evaluate the function at . Round to the nearest tenth. a. –1.7, 1.7, 0 c. –225.2, 225.2, 0 b. –225.2, 225.2, 0 d. 225.2, –225.2, 0

22. Use the function y = 50 tan x on the interval . Complete the ordered pair (x, 125). Round your answer to the nearest whole number. a. 90º b. 22º c. 2º d. 68º

23. Use a graphing calculator to solve the equation in the interval from . Round your

answers to the nearest hundredth. a. 1.21, 4.35 c. 1.21, 2.26, 3.31, 4.35, 5.40 b. 3.64 d. 0.404, 1,452.5, 3.55, 4.59, 5.64

24. Identify the period for and tell where two asymptotes occur for the function.

a. period = ; two asymptotes at x = – and x =

b. period = ; two asymptotes at x = and x =

c. period = ; two asymptotes at x = and x = 2

d. period = ; two asymptotes at x = 0 and x =

Graph the function in the interval from 0 to 2π.

25. y = –4 cos 4θ

a. c.

b. d.

26. Evaluate cot –105º. Round your answer to the nearest hundredth. a. –1.04 b. 0.27 c. 3.73 d. –3.86

27. Suppose . Find .

a. b. c. d. 176

28. Find the exact value of csc 135º. If the expression is undefined, write undefined. a. 0 b. undefined c. d.

29. Find the exact value of sec (–270º). If the expression is undefined, write undefined. a. undefined b. 1 c. 0 d. –1

30. Find the exact value of cot 45º. If the expression is undefined, write undefined. a. 0 b. 1 c. –1 d. undefined

31. Evaluate to the nearest hundredth. The angle is given in radians.

a. –0.58 b. 0.58 c. –1.73 d. 0

Short Answer

32. Consider the graph of the cosine function shown below.

a. Find the period and amplitude of the cosine function. b. At what values of for do the maximum value(s), minimum values(s), and zeros occur?

33. a. Sketch at least one cycle of a sine curve with amplitude 4 and period of 12 π. Assume a > 0.

b. Write an equation for the graph.

Algebra II B Review 5 Answer Section

MULTIPLE CHOICE

1. ANS: C OBJ: 13-2.1 Working With Angles in Standard Position

STA: MI A2.10.1 | MI A2.10.3

2. ANS: C OBJ: 13-2.1 Working With Angles in Standard Position STA: MI A2.10.1 | MI A2.10.3

3. ANS: B OBJ: 13-2.2 Using the Unit Circle STA: MI A2.10.1 | MI A2.10.3

4. ANS: B OBJ: 13-2.2 Using the Unit Circle STA: MI A2.10.1 | MI A2.10.3

5. ANS: D OBJ: 13-3.1 Using Radian Measure STA: MI A2.10.2 | MI A2.10.3

6. ANS: A OBJ: 13-3.1 Using Radian Measure STA: MI A2.10.2 | MI A2.10.3

7. ANS: A OBJ: 13-3.1 Using Radian Measure STA: MI A2.10.2 | MI A2.10.3

8. ANS: B OBJ: 13-3.1 Using Radian Measure STA: MI A2.10.2 | MI A2.10.3

9. ANS: C OBJ: 13-4.1 Interpreting Sine Functions STA: MI A2.10.4 | MI A2.10.5 | MI A3.1.1 | MI A3.1.2 | MI A3.1.3

10. ANS: C OBJ: 13-4.1 Interpreting Sine Functions STA: MI A2.10.4 | MI A2.10.5 | MI A3.1.1 | MI A3.1.2 | MI A3.1.3

11. ANS: A OBJ: 13-4.1 Interpreting Sine Functions STA: MI A2.10.4 | MI A2.10.5 | MI A3.1.1 | MI A3.1.2 | MI A3.1.3

12. ANS: B OBJ: 13-4.1 Interpreting Sine Functions STA: MI A2.10.4 | MI A2.10.5 | MI A3.1.1 | MI A3.1.2 | MI A3.1.3

13. ANS: C OBJ: 13-4.2 Graphing Sine Functions STA: MI A2.10.4 | MI A2.10.5 | MI A3.1.1 | MI A3.1.2 | MI A3.1.3

14. ANS: A OBJ: 13-4.2 Graphing Sine Functions STA: MI A2.10.4 | MI A2.10.5 | MI A3.1.1 | MI A3.1.2 | MI A3.1.3

15. ANS: A OBJ: 13-5.1 Graphing and Writing Cosine Functions STA: MI A2.10.4 | MI A2.10.5 | MI A3.1.1 | MI A3.1.2 | MI A3.1.3

16. ANS: D OBJ: 13-5.2 Solving Trigonometric Equations STA: MI A2.10.4 | MI A2.10.5 | MI A3.1.1 | MI A3.1.2 | MI A3.1.3

17. ANS: B OBJ: 13-5.2 Solving Trigonometric Equations STA: MI A2.10.4 | MI A2.10.5 | MI A3.1.1 | MI A3.1.2 | MI A3.1.3

18. ANS: C OBJ: 13-5.2 Solving Trigonometric Equations STA: MI A2.10.4 | MI A2.10.5 | MI A3.1.1 | MI A3.1.2 | MI A3.1.3

19. ANS: B OBJ: 13-6.1 Graphing the Tangent Function STA: MI A2.10.1

20. ANS: C OBJ: 13-6.1 Graphing the Tangent Function STA: MI A2.10.1

21. ANS: B OBJ: 13-6.1 Graphing the Tangent Function STA: MI A2.10.1

22. ANS: D OBJ: 13-6.1 Graphing the Tangent Function STA: MI A2.10.1

23. ANS: B OBJ: 13-6.1 Graphing the Tangent Function STA: MI A2.10.1

24. ANS: C OBJ: 13-6.1 Graphing the Tangent Function STA: MI A2.10.1

25. ANS: C OBJ: 13-5.1 Graphing and Writing Cosine Functions

STA: MI A2.10.4 | MI A2.10.5 | MI A3.1.1 | MI A3.1.2 | MI A3.1.3

26. ANS: B OBJ: 13-8.1 Evaluating Reciprocal Trigonometric Functions STA: MI A2.2.6

27. ANS: C OBJ: 13-8.1 Evaluating Reciprocal Trigonometric Functions STA: MI A2.2.6

28. ANS: D OBJ: 13-8.1 Evaluating Reciprocal Trigonometric Functions STA: MI A2.2.6

29. ANS: A OBJ: 13-8.1 Evaluating Reciprocal Trigonometric Functions STA: MI A2.2.6

30. ANS: B OBJ: 13-8.1 Evaluating Reciprocal Trigonometric Functions STA: MI A2.2.6

31. ANS: A OBJ: 13-8.1 Evaluating Reciprocal Trigonometric Functions STA: MI A2.2.6

SHORT ANSWER

32. ANS:

a. The period is 12 π and the amplitude is 4.

b. maximum values: 0 : 12 π : π :

32 π : 2π

minimum values: 14 π :

34 π :

54 π :

74 π

zeros: 18 π :

38 π :

58 π :

78 π :

98 π :

118 π :

138 π :

158 π

OBJ: 13-5.1 Graphing and Writing Cosine Functions STA: MI A2.10.4 | MI A2.10.5 | MI A3.1.1 | MI A3.1.2 | MI A3.1.3

33. ANS: a.

b. y = 4 sin 4θ

OBJ: 13-4.2 Graphing Sine Functions STA: MI A2.10.4 | MI A2.10.5 | MI A3.1.1 | MI A3.1.2 | MI A3.1.3