Math 141-142: Unit 5

Deadline: Thursday August 15 (141) or Thursday August 8 (142)

Topics

In this unit you will learn more about the trigonometric functions. In order to use them for solving real-world problems, you need to know more about their relationships with each other through the various trigonometric identities.

• Basic identities, including Pythagorean identities. (6.1)
• Identity verification and disproving false identities. (6.1)
• Sum and difference identities. (6.2)
• Cofunction identities. (6.2)
• Double-angle and half-angle identities. (6.3)
• Identities for products of sin and cos. (6.4)
• Identities for sums and differences of sin and cos. (6.4)

You will need to memorize the following formulas:

• Basic Identities (6.1)
• Sum, difference, and cofunction identities for sin and cos (6.2)
• Double-angle and half-angle identities for sin and cos (6.3)

When you take the Unit 5 exam, you can ask the lab consultant for a formula sheet with all of the other identities not listed above.

Study guidelines

• Section 6.1: Basic Identities and Their Use
  • Reading: pages 459-461.
    Read and work through examples 1-7 and their associated matched problems.
  • Problems: pages 459-461 #1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 33, 37, 39, 41, 43, 45, 47, 49, 57, 63, 65, 73, 77, 79, 89, 95, 97, 99
  • More practice problems, with solutions
    
    
• Section 6.2: Sum, Difference, and Cofunction Identities
  • Reading: pages 461-468.
    Read and work through examples 1-5 and their associated matched problems.
  • Problems: pages 468-470 #1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 53, 59, 61, 69, 73
  • More practice problems, with solutions
    
    
• Section 6.3: Double-Angle and Half-Angle Identities
  • Reading: pages 471-477.
    Read and work through examples 1-5 and their associated matched problems.
  • Problems: pages 477-480 #1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 45, 49, 53, 55, 57, 59, 73
  • More practice problems, with solutions
    
    
• Section 6.4: Product-Sum and Sum-Product Identities
  • Reading: pages 480-483.
    Read and work through examples 1-4 and their associated matched problems.
  • Problems: pages 483-485 #1, 3, 5, 7, 9, 11, 13, 15, 17, 21, 23, 25, 27, 45, 47, 49
  • More practice problems, with solutions
    
    
• Supplementary material (optional)
  • Schaum's Precalculus Outline, chapter 24 and part of chapter 23
  • Additional applications #1-4 for chapter 6, with answers
  • Additional exercises and demonstrations provided by other websites, for chapter 6
  • Answers to review problems from the textbook.
  • Calculator key stroke guides
  • The CD-ROM that came with yoqr textbook has tutorials, practice exams, and interesting "Interactive Diagrams".
  • Browse through the Archive Center on the NetTutor web site. Detailed solutions to selected problems are saved in the Archive Center.

Unit Exam #5

After completing the above work, do the following:

1. Read the exam description:
   • This exam has 16 questions, and will count 20 points toward your grade. 
   • This exam has a one hour time limit.
   • All questions on this exam require an exact answer. You should not try to use a calculator approximation for any of these questions.
   • Be sure to look under the entry box for the type of answer expected.
     • Some problems expect several answers. You have to enter these in the order requested in the problem, separated by commas. For example, if the question is What are cos x, sin x, tan x?, your answer might be 1/2,sqrt(3)/2,sqrt(3).
   • Make sure your calculator is set to the correct mode (radians or degrees) for each problem.
   • You will need to memorize the following formulas:
     • Basic Identities in section 6.1
     • Sum, Difference, and Cofunction Identities for sin and cos in section 6.2
     • Double-Angle and Half-Angle Identities for sin and cos in section 6.3
     When you take the exam, you can ask your proctor for a formula sheet with all of the other identities not listed above.
   • In previous classes, the more difficult topics were:
     • problems involving the half-angle identities, such as problems #39-42 on page 478
     • problems involving sum and difference identities for tangent.
2. Complete the online Unit 5 Pretest assignment for Math 141 or Math 142. You may use your book if you wish, and redo the pretest as many times as you like. Your pretest score will be scaled to 5 points maximum.
   • Directions: Click on the link above for your class, then choose the Unit 5 Pretest.
   • The pretest must be completed by the deadline date listed at the top of this page.
     However, you may redo the pretest as many times as you like before the due date.
     Your best score counts, and it will be rescaled to 5 points maximum.
3. If you are having trouble with any of the problems listed above or on the pretest or practice exams, make use of the help resources listed on the Help page.
4. Arrange with your proctor to take the online proctored Unit 5 Exam assignment for Math 141 or Math 142. Remember to bring identification, and remember that you will not be able to take the unit exam after the deadline date given at the top of this page. You may NOT use your book or notes on this exam.
   • Directions: Click on the link above for your class, then choose Unit 5 Exam.
   • The proctored unit exam must be completed by the deadline date listed at the top of this page, and may be repeated under certain conditions. See the Detailed Schedule page for Math 141 or Math 142 for specific rules.

   Note: Remember that you can always go back and take practice exams on this unit for Math 141 or Math 142 after the deadline has passed. In particular, this will help you prepare for the midterm and final exams.

   • Directions: Click on the link above for your class, then choose Unit 5 Exam. After the deadline has passed, this exam will be available in practice mode.

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