Final Exam Pre-Calculus - Somerset...
Transcript of Final Exam Pre-Calculus - Somerset...
Final Exam Pre-Calculus
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 1. If , find .
a. 8
5
c. 6
7
b. 13
5
d. 7
6
____ 2. Find the values of the six trigonometric functions for angle , when and .
a.
sin = 5
3, cos =
5
4, csc =
3
5, sec =
4
5, tan =
3
4, and cot =
4
3.
b. sin =
4
5, cos =
3
5, csc =
5
4, sec =
5
3, tan =
4
3, and cot =
3
4.
c. sin =
5
3, cos =
3
4, csc =
3
5, sec =
4
5, tan =
4
3, and cot =
5
4.
d. sin =
4
5, cos =
3
5, csc =
5
3, sec =
5
4, tan =
4
3, and cot =
4
3.
____ 3. Find the values of the six trigonometric functions for angle , when and .
a.
sin = 12
13, cos =
5
13, csc =
13
12, sec =
13
5, tan =
12
5, and cot =
5
12.
b. sin =
12
13, cos =
5
13, csc =
13
5, sec =
13
12, tan =
12
5, and cot =
12
5.
c. sin =
13
5, cos =
5
12, csc =
5
13, sec =
12
13, tan =
12
5, and cot =
13
12.
d. sin =
13
5, cos =
13
12, csc =
5
13, sec =
12
13, tan =
5
12, and cot =
12
5.
____ 4. If and find . Round to the nearest tenth.
a. c. b. d.
____ 5. If and , find . Round to the nearest tenth.
a. c. b. d.
____ 6. Solve by using the measurements , , and . Round measures of sides
to the nearest tenth and measures of angles to the nearest degree.
A
B Ca
bc
a. , , c. , ,
b. , , d. , ,
____ 7. Solve by using the measurements , , and . Round measures of
sides to the nearest tenth and measures of angles to the nearest degree.
P
Q Rp
qr
a. , , c. , ,
b. , , d. , ,
____ 8. Change 3.94 radians to degree measure. Round to the nearest tenth.
a. c. b. d.
____ 9. Change to radian measure in terms of .
a. 35
54
c. 35
36
b. 35
18
d. 35
72
____ 10. Write in degrees.
a. c. b. d.
____ 11. Write in degrees
a. c. b. d.
____ 12. Write –2160° in radians.
a. c.
b. d.
____ 13. Find one positive and one negative angle coterminal with an angle of 126°.
a. 486°, –234° c. 486°, –36
b. 526°, –54° d. 216°, –36°
____ 14. Find one positive and one negative angle coterminal with an angle of 106°.
a. 466°, –16 c. 474°, –74°
b. 466°, –254° d. 196°, –16°
____ 15. Find the least positive angle measurement that is coterminal with °.
a. ° c. °
b. ° d. °
____ 16. Suppose is an angle in the standard position whose terminal side is in Quadrant III and . Find
the exact values of the five remaining trigonometric functions of .
a. 17
15,
17
8,
15
17,
8
15, and
15
8
c. 17
8,
17
15,
8
17,
8
15, and
15
8
b. –8
17, –
15
17, –
17
15,
15
8, and
8
15
d. 15
17, –
8
17, –
17
15,
15
8, and
8
15
____ 17. Suppose is an angle in the standard position whose terminal side is in Quadrant IV and . Find
the exact values of the five remaining trigonometric functions of
a.
, , , ,
b. , , , ,
c. , , , ,
d. , , , ,
____ 18. Find the values of the six trigonometric functions of an angle in standard position if the point with coordinates
(10, 24) lies on its terminal side.
a. sin =
12
5, cos =
12
13, tan =
5
13
csc = 5
12, sec =
13
12, cot =
13
5
c. sin =
12
13, cos =
5
13, tan =
12
5
csc = 13
12, sec =
13
5, cot =
5
12
b. sin =
5
13, cos =
12
13, tan =
5
12
csc = 13
5, sec =
13
12, cot =
12
5
d. sin =
13
12, cos =
13
5, tan =
5
12
csc = 12
13, sec =
5
13, cot =
12
5
____ 19. Find the values of the six trigonometric functions of an angle in standard position if the point with coordinates
(5, 12) lies on its terminal side.
a. sin =
13
12, cos =
13
5, tan =
5
12
csc = 12
13, sec =
5
13, cot =
12
5
c. sin =
5
13, cos =
12
13, tan =
5
12
csc = 13
5, sec =
13
12, cot =
12
5
b. sin =
12
5, cos =
12
13, tan =
5
13
csc = 5
12, sec =
13
12, cot =
13
5
d. sin =
12
13, cos =
5
13, tan =
12
5
csc = 13
12, sec =
13
5, cot =
5
12
____ 20. Use the unit circle to find the value of .
a. c. b. undefined d.
____ 21. Find the exact value of .
a.
c.
b.
d.
____ 22. Find the exact value of .
a.
c.
b. d.
____ 23.
a. 2 c.
b.
d.
____ 24.
a.
c.
b.
d. 2
____ 25.
a.
c.
b.
d.
____ 26. Find the exact value of .
a. 1 c.
b.
d. 0
____ 27. Find the reference angle for 288
a. 89 c. 72
b. 59 d. 108
____ 28. Find the exact value of sin .
a.
c. undefined
b.
d.
____ 29. Use the unit circle to find the value of .
a. c. b. d. undefined
____ 30.
a.
c.
b. 2 d.
____ 31. Find the amplitude, period, and phase shift of
a. amplitude = –5
period =
phase shift = –8
7
b. amplitude = 10
period =
phase shift = 8
7
c. amplitude = –5
period =
phase shift = –8
7
d. amplitude = 5
period =
phase shift = 8
7
____ 32. Write an equation of the cosine function with amplitude 2 and period
a.
c.
b.
d.
____ 33. Find the amplitude of . Then graph the function.
a. amplitude:
90 180 270–90–180–270
0.5
1
1.5
2
2.5
–0.5
–1
–1.5
–2
–2.5
y
c. amplitude: does not exist
90 180 270–90–180–270
0.1
0.2
0.3
0.4
0.5
–0.1
–0.2
–0.3
–0.4
–0.5
y
b. amplitude:
90 180 270–90–180–270
0.1
0.2
0.3
0.4
0.5
–0.1
–0.2
–0.3
–0.4
–0.5
y
d. amplitude:
90 180 270–90–180–270
0.1
0.2
0.3
0.4
0.5
–0.1
–0.2
–0.3
–0.4
–0.5
y
____ 34. Find the amplitude of . Then graph the function.
a. amplitude: 9 c. amplitude: does not exist
90 180 270–90–180–270
2
4
6
8
10
12
–2
–4
–6
–8
–10
–12
y
90 180 270–90–180–270
2
4
6
8
10
12
–2
–4
–6
–8
–10
–12
y
b. amplitude: 9
90 180 270–90–180–270
2
4
6
8
10
12
–2
–4
–6
–8
–10
–12
y
d. amplitude: 1
90 180 270–90–180–270
2
4
6
8
10
12
–2
–4
–6
–8
–10
–12
y
____ 35. Given a triangle with a = , A = °, and B = °, what is the length of c? Round to the nearest tenth.
a. c. b. d.
____ 36. Given a triangle with b = , c = , and A = ° what is the length of a? Round to the nearest tenth.
a. c. b. d.
____ 37. Solve .
A
B C
, ,
a. , , c. , ,
b. , , d. , ,
____ 38. Determine whether should be solved by using the Law of Sines or the Law of Cosines. Then solve the
triangle.
A
B C
c b
a
, ,
a. Law of Sines; , ,
b. Law of Cosines; , ,
c. Law of Cosines; , ,
d. Law of Sines; , ,
____ 39. Determine whether should be solved by using the Law of Sines or the Law of Cosines. Then solve the
triangle.
A
B C
c b
a
, ,
a. Law of Cosines; , ,
b. Law of Cosines; , ,
c. Law of Sines; , ,
d. Law of Sines; , ,
____ 40. If and , find and
a. ,
c. ,
b. ,
d. ,
____ 41. If sin = 3
7, find csc .
a. –3 c.
3
7
b.
7
3
d. 7
____ 42. Simplify cos x – sin x cot x.
a. c. b. d.
____ 43. Simplify .
a. c. b. d.
____ 44. What basic trigonometric identity would you use to verify that tan x cos x = sin x?
a.
c.
b.
d.
____ 45. What basic trigonometric identity would you use to verify that cot x sin x = cos x?
a. c.
b.
d.
____ 46. What basic trigonometric identity would you use to verify that ?
a.
c.
b. d.
____ 47. What basic trigonometric identity would you use to verify that ?
a. sin x = cos x tan x c.
b. d.
____ 48. What basic trigonometric identity would you use to verify that ?
a.
c. sin x = cos x tan x
b. d.
____ 49. Simplify
a. c. 0
b. d.
Final Exam Pre-Calculus
Answer Section
MULTIPLE CHOICE
1. ANS: B PTS: 1 DIF: Average REF: Lesson 4-1
OBJ: 4-1.1 Find values of trigonometric functions for acute angles of right triangles.
NAT: 3 STA: MA.912.T.1.3 | MA.912.T.2.1 TOP: Right Triangle Trigonometry
KEY: Trigonometry | Trigonometric Ratios
NOT: Example 2: Use One Trigonometric Value to Find Others
2. ANS: B PTS: 1 DIF: Average REF: Lesson 4-1
OBJ: 4-1.1 Find values of trigonometric functions for acute angles of right triangles.
NAT: 3 STA: MA.912.T.1.3 | MA.912.T.2.1 TOP: Right Triangle Trigonometry
KEY: Trigonometric Functions | Acute Angles
NOT: Example 1: Find Values of Trigonometric Ratios
3. ANS: A PTS: 1 DIF: Average REF: Lesson 4-1
OBJ: 4-1.1 Find values of trigonometric functions for acute angles of right triangles.
NAT: 3 STA: MA.912.T.1.3 | MA.912.T.2.1 TOP: Right Triangle Trigonometry
KEY: Trigonometric Functions | Acute Angles
NOT: Example 1: Find Values of Trigonometric Ratios
4. ANS: D PTS: 1 DIF: Average REF: Lesson 4-1
OBJ: 4-1.2 Solve right triangles. NAT: 3 STA: MA.912.T.1.4
TOP: Right Triangle Trigonometry KEY: Trigonometry | Trigonometric Ratios | Right Triangles
NOT: Example 3: Find a Missing Side Length
5. ANS: A PTS: 1 DIF: Average REF: Lesson 4-1
OBJ: 4-1.2 Solve right triangles. NAT: 3 STA: MA.912.T.1.4
TOP: Right Triangle Trigonometry KEY: Find Angle Measurements
NOT: Example 5: Find a Missing Angle Measure
6. ANS: D PTS: 1 DIF: Advanced REF: Lesson 4-1
OBJ: 4-1.2 Solve right triangles. NAT: 3 STA: MA.912.T.1.4
TOP: Right Triangle Trigonometry KEY: Solve Triangles | Right Triangles
NOT: Example 8: Solve a Right Triangle
7. ANS: A PTS: 1 DIF: Advanced REF: Lesson 4-1
OBJ: 4-1.2 Solve right triangles. NAT: 3 STA: MA.912.T.1.4
TOP: Right Triangle Trigonometry KEY: Solve Triangles | Right Triangles
NOT: Example 8: Solve a Right Triangle
8. ANS: C PTS: 1 DIF: Average REF: Lesson 4-2
OBJ: 4-2.1 Convert degree measures of angles to radian measures, and vice versa.
NAT: 3 STA: MA.912.T.1.1 TOP: Degrees and Radians
KEY: Angle Measures | Degree Measures | Radian Measures
NOT: Example 2: Convert Between Degree and Radian Measures
9. ANS: C PTS: 1 DIF: Average REF: Lesson 4-2
OBJ: 4-2.1 Convert degree measures of angles to radian measures, and vice versa.
NAT: 3 STA: MA.912.T.1.1 TOP: Degrees and Radians
KEY: Angle Measures | Degree Measures | Radian Measures
NOT: Example 2: Convert Between Degree and Radian Measures
10. ANS: C PTS: 1 DIF: Basic REF: Lesson 4-2
OBJ: 4-2.1 Convert degree measures of angles to radian measures, and vice versa.
NAT: 3 STA: MA.912.T.1.1 TOP: Degrees and Radians
KEY: Radian Measure | Degree Measures
NOT: Example 2: Convert Between Degree and Radian Measures
11. ANS: B PTS: 1 DIF: Basic REF: Lesson 4-2
OBJ: 4-2.1 Convert degree measures of angles to radian measures, and vice versa.
NAT: 3 STA: MA.912.T.1.1 TOP: Degrees and Radians
KEY: Radian Measure | Degree Measures
NOT: Example 2: Convert Between Degree and Radian Measures
12. ANS: B PTS: 1 DIF: Average REF: Lesson 4-2
OBJ: 4-2.1 Convert degree measures of angles to radian measures, and vice versa.
NAT: 3 STA: MA.912.T.1.1 TOP: Degrees and Radians
KEY: Radian Measure | Degree Measures
NOT: Example 2: Convert Between Degree and Radian Measures
13. ANS: A PTS: 1 DIF: Basic REF: Lesson 4-2
OBJ: 4-2.1 Convert degree measures of angles to radian measures, and vice versa.
NAT: 3 STA: MA.912.T.1.1 TOP: Degrees and Radians
KEY: Coterminal Angles NOT: Example 3: Find and Draw Coterminal Angles
14. ANS: B PTS: 1 DIF: Basic REF: Lesson 4-2
OBJ: 4-2.1 Convert degree measures of angles to radian measures, and vice versa.
NAT: 3 STA: MA.912.T.1.1 TOP: Degrees and Radians
KEY: Coterminal Angles NOT: Example 3: Find and Draw Coterminal Angles
15. ANS: C PTS: 1 DIF: Average REF: Lesson 4-2
OBJ: 4-2.2 Use angle measure to solve real-world problems. NAT: 3
STA: MA.912.T.3.4 TOP: Degrees and Radians
KEY: Coterminal Angles NOT: Example 3: Find and Draw Coterminal Angles
16. ANS: D
Feedback
A These are the inverse values. B Ensure that the correct trigonometric functions were used when calculating. C Ensure that the correct trigonometric functions were used when calculating. D Correct!
PTS: 1 DIF: Average REF: Lesson 4-3
OBJ: 4-3.1 Find values of trigonometric functions for any angle.
NAT: 3 STA: MA.912.T.2.1
TOP: Trigonometric Functions on the Unit Circle
KEY: Trigonometric Functions | Trigonometric Ratios
NOT: Example 2: Evaluate Trigonometric Functions of Quadrantal Angles
17. ANS: B
Feedback
A Check the ratios again. Some parts are correct and some are not. B Correct! C Check the ratios again. Some parts are correct and some are not. D These are the inverses of the correct answers.
PTS: 1 DIF: Average REF: Lesson 4-3
OBJ: 4-3.1 Find values of trigonometric functions for any angle.
NAT: 3 STA: MA.912.T.2.1
TOP: Trigonometric Functions on the Unit Circle
KEY: Trigonometric Functions | Trigonometric Ratios
NOT: Example 2: Evaluate Trigonometric Functions of Quadrantal Angles
18. ANS: C
Feedback
A Please review the trigonometric ratios. B There is confusion between the sine and cosine values. C Correct! D These are the inverses of the correct answers.
PTS: 1 DIF: Average REF: Lesson 4-3
OBJ: 4-3.1 Find values of trigonometric functions for any angle.
NAT: 3 STA: MA.912.T.2.1
TOP: Trigonometric Functions on the Unit Circle
KEY: Trigonometry | Trigonometric Functions | Unit Circle
NOT: Example 7: Find Trigonometric Values Using the Unit Circle
19. ANS: D PTS: 1 DIF: Average REF: Lesson 4-3
OBJ: 4-3.1 Find values of trigonometric functions for any angle.
NAT: 3 STA: MA.912.T.2.1
TOP: Trigonometric Functions on the Unit Circle
KEY: Trigonometry | Trigonometric Functions | Unit Circle
NOT: Example 7: Find Trigonometric Values Using the Unit Circle
20. ANS: A PTS: 1 DIF: Average REF: Lesson 4-3
OBJ: 4-3.2 Find values of trigonometric functions using the unit circle.
NAT: 3 STA: MA.912.T.1.2
TOP: Trigonometric Functions on the Unit Circle
KEY: Trigonometry | Trigonometric Functions | Unit Circle
NOT: Example 2: Evaluate Trigonometric Functions of Quadrantal Angles
21. ANS: B PTS: 1 DIF: Average REF: Lesson 4-3
OBJ: 4-3.2 Find values of trigonometric functions using the unit circle.
NAT: 3 STA: MA.912.T.1.2
TOP: Trigonometric Functions on the Unit Circle
KEY: Circular Functions | Unit Circle | Periodic Functions
NOT: Example 8: Use the Periodic Nature of Circular Functions
22. ANS: C PTS: 1 DIF: Average REF: Lesson 4-3
OBJ: 4-3.2 Find values of trigonometric functions using the unit circle.
NAT: 3 STA: MA.912.T.1.2
TOP: Trigonometric Functions on the Unit Circle
KEY: Circular Functions | Unit Circle | Periodic Functions
NOT: Example 8: Use the Periodic Nature of Circular Functions
23. ANS: A PTS: 1 DIF: Average REF: Lesson 4-3
OBJ: 4-3.2 Find values of trigonometric functions using the unit circle.
NAT: 3 STA: MA.912.T.1.2
TOP: Trigonometric Functions on the Unit Circle
KEY: Circular Functions | Unit Circle | Periodic Functions
NOT: Example 8: Use the Periodic Nature of Circular Functions
24. ANS: C PTS: 1 DIF: Average REF: Lesson 4-3
OBJ: 4-3.2 Find values of trigonometric functions using the unit circle.
NAT: 3 STA: MA.912.T.1.2
TOP: Trigonometric Functions on the Unit Circle
KEY: Circular Functions | Unit Circle | Periodic Functions
NOT: Example 8: Use the Periodic Nature of Circular Functions
25. ANS: C PTS: 1 DIF: Average REF: Lesson 4-3
OBJ: 4-3.2 Find values of trigonometric functions using the unit circle.
NAT: 3 STA: MA.912.T.1.2
TOP: Trigonometric Functions on the Unit Circle
KEY: Circular Functions | Unit Circle | Periodic Functions
NOT: Example 8: Use the Periodic Nature of Circular Functions
26. ANS: B
[Change angle measure to one that is on the unit circle]
PTS: 1 DIF: Basic REF: Lesson 4-3
OBJ: 4-3.2 Find values of trigonometric functions using the unit circle.
NAT: 3 STA: MA.912.T.1.2
TOP: Trigonometric Functions on the Unit Circle
KEY: Trigonometric Functions | Unit Circle
NOT: Example 8: Use the Periodic Nature of Circular Functions
27. ANS: C
Feedback
A This is too large to be the reference angle. B This is too small to be the reference angle. C Correct! D The reference angle refers to 360 degrees, not 180 degrees.
PTS: 1 DIF: Average REF: Lesson 4-3
OBJ: 4-3.2 Find values of trigonometric functions using the unit circle.
NAT: 3 STA: MA.912.T.1.2
TOP: Trigonometric Functions on the Unit Circle
KEY: Trigonometric Functions | Trigonometric Ratios NOT: Example 3: Find Reference Angles
28. ANS: B
Feedback
A Close, the correct answer has the opposite sign. B Correct! C This value is defined. Check your calculations again. D Check the calculations again. This is incorrect.
PTS: 1 DIF: Average REF: Lesson 4-3
OBJ: 4-3.2 Find values of trigonometric functions using the unit circle.
NAT: 3 STA: MA.912.T.1.2
TOP: Trigonometric Functions on the Unit Circle
KEY: Trigonometric Functions | Trigonometric Ratios
NOT: Example 7: Find Trigonometric Values Using the Unit Circle
29. ANS: B PTS: 1 DIF: Average REF: Lesson 4-3
OBJ: 4-3.2 Find values of trigonometric functions using the unit circle.
NAT: 3 STA: MA.912.T.1.2
TOP: Trigonometric Functions on the Unit Circle
KEY: Trigonometry | Trigonometric Functions | Unit Circle
NOT: Example 2: Evaluate Trigonometric Functions of Quadrantal Angles
30. ANS: C PTS: 1 DIF: Average REF: Lesson 4-3
OBJ: 4-3.2 Find values of trigonometric functions using the unit circle.
NAT: 3 STA: MA.912.T.1.2
TOP: Trigonometric Functions on the Unit Circle
KEY: Circular Functions | Unit Circle | Periodic Functions
NOT: Example 8: Use the Periodic Nature of Circular Functions
31. ANS: D PTS: 1 DIF: Average REF: Lesson 4-4
OBJ: 4-4.1 Graph transformations of the sine and cosine functions.
NAT: 2 STA: MA.912.A.2.10 | MA.912.T.1.6
TOP: Graphing Sine and Cosine Functions
KEY: Amplitude | Period | Sine Functions | Cosine Functions
NOT: Example 5: Graph Horizontal Translations of Sinusoidal Functions
32. ANS: C PTS: 1 DIF: Average REF: Lesson 4-4
OBJ: 4-4.1 Graph transformations of the sine and cosine functions.
NAT: 2 STA: MA.912.A.2.10 | MA.912.T.1.6
TOP: Graphing Sine and Cosine Functions
KEY: Sine Functions | Cosine Functions | Amplitude | Period
NOT: Example 3: Graph Horizontal Dilations of Sinusoidal Functions
33. ANS: D PTS: 1 DIF: Basic REF: Lesson 4-4
OBJ: 4-4.1 Graph transformations of the sine and cosine functions.
NAT: 2 STA: MA.912.A.2.10 | MA.912.T.1.6
TOP: Graphing Sine and Cosine Functions KEY: Amplitude | Sine | Cosine
NOT: Example 1: Graph Vertical Dilations of Sinusoidal Functions
34. ANS: B PTS: 1 DIF: Basic REF: Lesson 4-4
OBJ: 4-4.1 Graph transformations of the sine and cosine functions.
NAT: 2 STA: MA.912.A.2.10 | MA.912.T.1.6
TOP: Graphing Sine and Cosine Functions KEY: Amplitude | Sine | Cosine
NOT: Example 1: Graph Vertical Dilations of Sinusoidal Functions
35. ANS: B PTS: 1 DIF: Average REF: Lesson 4-7
OBJ: 4-7.1 Solve oblique triangles by using the Law of Sines ore the Law of Cosines.
NAT: 3 STA: MA.912.T.2.3
TOP: The Law of Sines and the Law of Cosines KEY: Solve Triangles | Law of Sines
NOT: Example 1: Apply the Law of Sines (AAS)
36. ANS: C PTS: 1 DIF: Average REF: Lesson 4-7
OBJ: 4-7.1 Solve oblique triangles by using the Law of Sines ore the Law of Cosines.
NAT: 3 STA: MA.912.T.2.3
TOP: The Law of Sines and the Law of Cosines KEY: Solve Triangles | Law of Cosines
NOT: Example 6: Apply the Law of Cosines (SAS)
37. ANS: C PTS: 1 DIF: Average REF: Lesson 4-7
OBJ: 4-7.1 Solve oblique triangles by using the Law of Sines ore the Law of Cosines.
NAT: 3 STA: MA.912.T.2.3
TOP: The Law of Sines and the Law of Cosines KEY: Solve Triangles | Law of Sines
NOT: Example 1: Apply the Law of Sines (AAS)
38. ANS: C PTS: 1 DIF: Average REF: Lesson 4-7
OBJ: 4-7.1 Solve oblique triangles by using the Law of Sines ore the Law of Cosines.
NAT: 3 STA: MA.912.T.2.3
TOP: The Law of Sines and the Law of Cosines KEY: Solve Triangles | Law of Cosines
NOT: Example 5: Apply the Law of Cosines (SSS)
39. ANS: A PTS: 1 DIF: Average REF: Lesson 4-7
OBJ: 4-7.1 Solve oblique triangles by using the Law of Sines ore the Law of Cosines.
NAT: 3 STA: MA.912.T.2.3
TOP: The Law of Sines and the Law of Cosines KEY: Solve Triangles | Law of Cosines
NOT: Example 5: Apply the Law of Cosines (SSS)
40. ANS: C PTS: 1 DIF: Average REF: Lesson 5-1
OBJ: 5-1.1 Identify and use basic trigonometric identities to find trigonometric values.
NAT: 3 STA: MA.912.T.3.2 TOP: Trigonometric Identities
KEY: Reciprocal Identities | Quotient Identities | Pythagorean Identities | Symmetry Identities |
Opposite-Angle Identities NOT: Example 2: Use Pythagorean Identities
41. ANS: B
Feedback
A The answer should be the reciprocal of the original value. B Correct! C The answer should be the reciprocal of the original value. D The answer should be the reciprocal of the original value.
PTS: 1 DIF: Average REF: Lesson 5-1
OBJ: 5-1.1 Identify and use basic trigonometric identities to find trigonometric values.
NAT: 3 STA: MA.912.T.3.2 TOP: Trigonometric Identities
KEY: Reciprocal Identities | Trigonometric Identities
NOT: Example 1: Use Reciprocal and Quotient Identities
42. ANS: B PTS: 1 DIF: Average REF: Lesson 5-1
OBJ: 5-1.2 Use basic trigonometric identities to simplify and rewrite trigonometric expressions.
NAT: 3 STA: MA.912.T.3.2 TOP: Trigonometric Identities
KEY: Trigonometric Identities | Simplify Trigonometric Expressions
NOT: Example 4: Simplify by Rewriting Using Only Sine and Cosine
43. ANS: A
Feedback
A Correct! B Watch your signs. C Watch your basic trig identities. D Watch your signs and identities.
PTS: 1 DIF: Average REF: Lesson 5-2
OBJ: 5-2.1 Verify trigonometric identities. NAT: 3
STA: MA.912.T.3.2 TOP: Verifying Trigonmetric Identities
KEY: Verify Trigonometric Identities
NOT: Example 2: Verify a Trigonometric Identity by Combining Fractions
44. ANS: D PTS: 1 DIF: Average REF: Lesson 5-2
OBJ: 5-2.1 Verify trigonometric identities. NAT: 3
STA: MA.912.T.3.2 TOP: Verifying Trigonmetric Identities
KEY: Trigonometric Identities | Verify Identities
NOT: Example 1: Verify a Trigonometric Identity
45. ANS: B PTS: 1 DIF: Average REF: Lesson 5-2
OBJ: 5-2.1 Verify trigonometric identities. NAT: 3
STA: MA.912.T.3.2 TOP: Verifying Trigonmetric Identities
KEY: Trigonometric Identities | Verify Identities
NOT: Example 1: Verify a Trigonometric Identity
46. ANS: C PTS: 1 DIF: Average REF: Lesson 5-2
OBJ: 5-2.1 Verify trigonometric identities. NAT: 3
STA: MA.912.T.3.2 TOP: Verifying Trigonmetric Identities
KEY: Trigonometric Identities | Verify Identities
NOT: Example 1: Verify a Trigonometric Identity
47. ANS: C PTS: 1 DIF: Average REF: Lesson 5-2
OBJ: 5-2.1 Verify trigonometric identities. NAT: 3
STA: MA.912.T.3.2 TOP: Verifying Trigonmetric Identities
KEY: Trigonometric Identities | Verify Identities
NOT: Example 1: Verify a Trigonometric Identity
48. ANS: A PTS: 1 DIF: Average REF: Lesson 5-2
OBJ: 5-2.1 Verify trigonometric identities. NAT: 3
STA: MA.912.T.3.2 TOP: Verifying Trigonmetric Identities
KEY: Trigonometric Identities | Verify Identities
NOT: Example 1: Verify a Trigonometric Identity
49. ANS: A
Feedback
A Correct! B Watch your signs. C Watch your identities. D Check your multiplication.
PTS: 1 DIF: Average REF: Lesson 5-2
OBJ: 5-2.2 Determine whether equations are identities. NAT: 3
STA: MA.912.T.3.2 TOP: Verifying Trigonmetric Identities
KEY: Trigonometric Identities
NOT: Example 3: Verify a Trigonometric Identity by Multiplying