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Name: ______________________ Class: _________________ Date: _________ ID: A Trigonometry Test #2 Review 1. Solve ΔABC using the diagram and the given measurements. (The triangle is not drawn to scale.) B = 42°, a = 17 2. Solve triangle ABC given that A = 47°, B = 52°, and b = 78. ____ 3. Solve triangle ABC given that A = 45°, B = 54°, and b = 70. a. C = 81°, a = 80.09, c = 97.78 c. C = 81°, a = 61.18, c = 85.46 b. C = 261°, a = 61.18, c = 85.46 d. C = 261°, a = 80.09, c = 97.78 4. Find the area of ΔABC. The figure is not drawn to scale. 5. Solve ΔABC with A = 110°, a = 5, and b = 7.3. ____ 6. Solve ΔABC with A = 69°, b = 34, and c = 46. a. a = 46.38, B = 43.19°, C = 67.81° c. b. a = 46.38, B = 41.74°, C = 69.26° d. a = 45.15, B = 43.19°, C = 67.81° a = 45.15, B = 41.74°, C = 69.26° 7. Solve triangle ABC given that a = 19, b = 10, and c = 14. 1 Name: ______________________ ID: A 8. Find the area of ΔABC . ____ 9. Determine the graph of: y = cos x a. b. c. d. 2 Name: ______________________ ____ 10. Determine the graph of : y = 2 sin x a. b. ID: A c. d. Find the amplitude and period of the graph. 11. y = 3 sin 2 πx 12. y = −3 cos πx 3 Name: ______________________ ID: A 13. Graph y = tan x. Include vertical asymptotes in your sketch. Be sure to pay attention to the horizontal axis to determine whether you should graph in degrees or radians! 1 x. Include vertical asymptotes in your sketch. Be sure to pay attention to the horizontal 2 axis to determine whether you should graph in degrees or radians! 14. Graph y = tan 15. a. Graph y = sin x and y = sin (–x) on a graphing calculator. b. Graph y = –sin x and y = sin (–x) on a graphing calculator. c. Graph y = cos x and y = cos (–x) on a graphing calculator. d. Graph y = –cos x and y = cos (–x) on a graphing calculator. e. Describe any patterns that you observed in your graphs. Be sure to include comments about which graphs are the same and which are reflections of each other. 16. Compare the graphs of y = cos x, y = 4 cos x, and y = cos 4x. Specifically compare the amplitude and period of the graphs. 17. Consider the related equations y = sin x, y = 2 sin x, and y = sin 2x. Explain the effect that the coefficient 2 has on the graphs of y = 2 sin x and y = sin 2x when compared to the graph of y = sin x. 4 Name: ______________________ ID: A ÁÊ π ˜ˆ ____ 18. Graph y = 4 cos ÁÁÁÁ x − ˜˜˜˜ on the interval −π ≤ x ≤ π. ÁË 4 ˜¯ a. c. b. d. 5 Name: ______________________ ID: A Graph: ÊÁ π ˆ˜ ____ 19. y = −tan ÁÁÁÁ x + ˜˜˜˜ ÁË 2 ˜¯ a. b. c. d. 6 none of these ID: A Trigonometry Test #2 Review Answer Section 1. ANS: A = 48°, b = 15.31, c = 22.88 PTS: 1 DIF: Level B REF: MAL21702 TOP: Lesson 13.1 Use Trigonometry with Right Triangles KEY: solve | trigonometry | right triangle BLM: Comprehension NOT: 978-0-618-65615-8 2. ANS: C = 81°, a = 72.39, c = 97.76 PTS: 1 DIF: Level B REF: TOP: Lesson 13.5 Apply the Law of Sines BLM: Comprehension NOT: 3. ANS: C PTS: 1 DIF: TOP: Lesson 13.5 Apply the Law of Sines BLM: Comprehension NOT: 4. ANS: 2 14.67 cm MAL21756 KEY: solve | triangle | Law of Sines 978-0-618-65615-8 Level B REF: MAL21757 KEY: solve | triangle | Law of Sines 978-0-618-65615-8 PTS: 1 DIF: Level B REF: MAL21768 TOP: Lesson 13.5 Apply the Law of Sines KEY: area | acute | triangle | trigonometry | sine | SAS BLM: Comprehension NOT: 978-0-618-65615-8 5. ANS: No solution. It is not possible to draw the indicated triangle. PTS: 1 DIF: Level B REF: TOP: Lesson 13.5 Apply the Law of Sines BLM: Comprehension NOT: 6. ANS: A PTS: 1 DIF: TOP: Lesson 13.6 Apply the Law of Cosines BLM: Comprehension NOT: 7. ANS: A = 103.4°, B = 30.8°, C = 45.8° PTS: TOP: KEY: NOT: A2.13.05.FR.11 KEY: Free response | law of sines | SSA 978-0-618-65615-8 Level B REF: MAL21778 KEY: Law of Cosines | solve 978-0-618-65615-8 1 DIF: Level B REF: MAL21779 Lesson 13.6 Apply the Law of Cosines triangle | Law of Sines | Law of Cosines BLM: Comprehension 978-0-618-65615-8 1 ID: A 8. ANS: 276.96 PTS: 1 DIF: Level B REF: MAL21785 TOP: Lesson 13.6 Apply the Law of Cosines KEY: BLM: Comprehension NOT: 978-0-618-65615-8 9. ANS: B PTS: 1 DIF: Level B REF: TOP: Lesson 14.1 Graph Sine, Cosine, and Tangent Functions KEY: graph | trigonometry | cosine BLM: Knowledge NOT: 10. ANS: A PTS: 1 DIF: Level B REF: TOP: Lesson 14.1 Graph Sine, Cosine, and Tangent Functions KEY: graph | trigonometry | sine BLM: Knowledge NOT: 11. ANS: Amplitude: 3 Period: 1 area | heron | triangle MAL21793 978-0-618-65615-8 MAL21791 978-0-618-65615-8 PTS: 1 DIF: Level A REF: MAL21800 TOP: Lesson 14.1 Graph Sine, Cosine, and Tangent Functions KEY: period | amplitude | sin BLM: Knowledge NOT: 978-0-618-65615-8 12. ANS: Amplitude: 3 Period: 2 PTS: 1 DIF: Level A REF: MAL21801 TOP: Lesson 14.1 Graph Sine, Cosine, and Tangent Functions KEY: period | amplitude | cos BLM: Knowledge NOT: 978-0-618-65615-8 13. ANS: PTS: 1 DIF: Level B REF: MAL21809 TOP: Lesson 14.1 Graph Sine, Cosine, and Tangent Functions KEY: tangent | graph BLM: Knowledge NOT: 978-0-618-65615-8 2 ID: A 14. ANS: PTS: 1 DIF: Level B REF: MAL21810 TOP: Lesson 14.1 Graph Sine, Cosine, and Tangent Functions KEY: graph | tangent BLM: Knowledge NOT: 978-0-618-65615-8 15. ANS: e. The graphs of y = –sin x and y = sin (–x) are the same. The graphs of y = –sin x and y = sin (–x) are reflections over the x-axis of the graph of y = sin x. The graphs of y = cos x and y = cos (–x) are the same. The graphs of y = cos x and y = cos(–x) are reflections over the x-axis of the graph of y = –cos x. PTS: NAT: TOP: KEY: NOT: 1 DIF: Level C REF: MAL21798 NCTM 9-12.NOP.3.a | NCTM 9-12.GEO.4.e Lesson 14.1 Graph Sine, Cosine, and Tangent Functions characteristics | graph | cosine | sine | amplitude BLM: Analysis 978-0-618-65615-8 3 ID: A 16. ANS: The graphs of y = cos x and y = cos 4x have an amplitude of 1, while the graph of y = 4 cos x has an amplitude of 4. The graphs of y = cos x and y = 4 cos x both have a period of 360°, while the graph of y = cos 4x has a period of 90°. PTS: 1 DIF: Level B REF: MAL21796 NAT: NCTM 9-12.CON.2 | NCTM 9-12.PRS.1 | NCTM 9-12.GEO.4.e TOP: Lesson 14.1 Graph Sine, Cosine, and Tangent Functions KEY: cosine | frequency | period | amplitude | compare | graph BLM: Comprehension NOT: 978-0-618-65615-8 17. ANS: In the equation y = 2 sin x, the 2 is the amplitude of the function. So the graph of y = 2 sin x is bounded by the lines y = 2 and y = –2, rather than y = 1 and y = –1 as in the graph of y = sin x. In the equation y = sin 2x, the 2 represents the frequency and therefore determines the period (in this case, π ). So the graph of y = sin 2x completes one cycle in π units, which is twice the frequency of the graph of y = sin x which has a period of 2π. PTS: NAT: TOP: KEY: NOT: 18. ANS: TOP: KEY: 19. ANS: TOP: KEY: 1 DIF: Level B REF: MAL21797 NCTM 9-12.CON.2 | NCTM 9-12.PRS.4 | NCTM 9-12.PRS.1 | NCTM 9-12.GEO.4.e Lesson 14.1 Graph Sine, Cosine, and Tangent Functions amplitude | characteristics | period | sine BLM: Comprehension 978-0-618-65615-8 A PTS: 1 DIF: Level B REF: MAL21816 Lesson 14.2 Translate and Reflect Trigonometric Graphs graph | sine | cosine BLM: Knowledge NOT: 978-0-618-65615-8 C PTS: 1 DIF: Level B REF: MAL21819 Lesson 14.2 Translate and Reflect Trigonometric Graphs tangent | graph BLM: Knowledge NOT: 978-0-618-65615-8 4