MHF4U Unit 6 Test - Trigonometric Equations and Identities PDF

MHF4U: Advanced Functions Unit 6 Test: Functions – Trigonometric Equations and Identities Name: Date:. Category Total Marks Marks Obtain...

MHF4U: Advanced Functions Unit 6 Test: Functions – Trigonometric Equations and Identities Name: Date:. Category Total Marks Marks Obtained Knowledge and Understanding 13 Thinking 10 Communication 10 Application 14 The following curriculum expectations are covered in this evaluation: B1, B2, B3 Knowledge & Understanding: 1. Which of the following is the correct compound angle formula for cos ( + ) (Mark Value: 3) a. cos  sin  - cos  sin  b. cos  sin  + cos  sin  c. cos  cos  - sin  sin  d. cos  sin  + cos  sin  2. Which of the following is not true about trigonometric identities? (Mark Value: 3) a. The left and right sides of the identity must be modified independently b. It is usually easier to start working with the simpler side of the identity c. It is often useful to start by changing all trigonometric ratios to sine or cosine d. The identity can be simplified by finding a common denominator, factoring, expanding, or cancelling out terms. 3. Which of the following is not a solution to the equation sin x = 0, 0 ≤ x ≤ 2 (Mark Value: 3) a. x = 0  b. x = c. x =  This study source was downloaded by 100000873450430 from CourseHero.com on 11-25-2024 14:05:08 GMT -06:00 https://www.coursehero.com/file/82400033/MHF4U-online-Unit-6-Testpdf/  d. x = 2 4. a. Determine a simplified expression for cos ( ) b. Determine the exact value of sin ( ) (Mark Value: 4) Thinking: 5. The depth of the tide on the edge of a lake can be modelled by the function , where d is depth of water in meters and t is the time in hours, if 0 ≤ t ≤ 24. Consider a day when t = 0 represents midnight. Determine the times at which the depth of the water is 3 meters. (Mark Value: 4) This study source was downloaded by 100000873450430 from CourseHero.com on 11-25-2024 14:05:08 GMT -06:00 https://www.coursehero.com/file/82400033/MHF4U-online-Unit-6-Testpdf/  6. Which of the following expressions is equivalent to sin 2x? (Mark Value: 3) a. sinx sinx – cosx cosx b. sinx cosx c. sinx sinx + cosx cosx d. 2 sinx cosx 7. Prove the following trigonometric identities: (Mark Value: 6) a. b. c. This study source was downloaded by 100000873450430 from CourseHero.com on 11-25-2024 14:05:08 GMT -06:00 https://www.coursehero.com/file/82400033/MHF4U-online-Unit-6-Testpdf/  Communication: 8. Explain how to use special triangles as well as the CAST rule to determine the exact value of trigonometric expression. (Mark Value: 3) 9. Using a graph, explain why the trigonometric equation sin x = 0 has an infinite number of solutions when - < x < . (Mark Value: 4) 10. Determine whether or not – cos x (tan x)5 = sin x (tan x)2 is a trigonometric identity. Explain how you know. (Mark Value: 4) This study source was downloaded by 100000873450430 from CourseHero.com on 11-25-2024 14:05:08 GMT -06:00 https://www.coursehero.com/file/82400033/MHF4U-online-Unit-6-Testpdf/  Application: 11. Which of the following is equivalent to the expression sin 2x cos x – sin x cos 2x? a. b. c. d. (Mark Value: 3) 11. Angles  and  are obtuse angles in quadrant II. If csc  = 3 and tan  = , determine the exact value of cos ( + ). (Mark Value: 5) This study source was downloaded by 100000873450430 from CourseHero.com on 11-25-2024 14:05:08 GMT -06:00 https://www.coursehero.com/file/82400033/MHF4U-online-Unit-6-Testpdf/  13. Solve the following trigonometric equations for x if 0 ≤ x ≤ 2: (Mark Value: 6) a. 2 sinx = b. 5 + 4 cos c. (tan x)2 = 2 + tan x This study source was downloaded by 100000873450430 from CourseHero.com on 11-25-2024 14:05:08 GMT -06:00 https://www.coursehero.com/file/82400033/MHF4U-online-Unit-6-Testpdf/ Powered by TCPDF (www.tcpdf.org)