Math 141-142: Unit 5

Note: The information on this page is for the 7th edition of the textbook.
Click here for the 6th edition information.

Table of Contents:

Topics
Study Guidelines
Unit Pretest and Exam Description
Checklist

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 (6.3)
• Identity verification and disproving false identities (6.3)
• Sum and difference formulas (6.4)
• Cofunction identities (identities 3(a) and 3(b)) (6.4)
• Double-angle and half-angle formulas (6.5)
• Product-to-Sum Formulas (6.6)
• Sum-to-Product Formulas (6.6)

You will need to memorize the following formulas:

• Basic Identities (pages 430-431 in section 6.3)
• Sum, difference, and cofunction identities for sin and cos (formulas 1-5 in section 6.4)
• Double-angle and half-angle identities for sin and cos (formulas 1-4, 6, 7, 10ab in section 6.5)

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 for the 7th edition of Sullivan's Precalculus

These reading and problem assignments are designed to help you learn the course material. You should complete all of these problems, check your answers in the back of the textbook, and get help with the problems that you missed. Most of the problems are odd-numbered, so you can check the solutions in the Solutions Manual.

The only way to learn mathematics is to do mathematics, so while these problems will not be collected or graded, you will probably not do well in the course if you do not complete these and check your work as described above. After completing these problems, go on to the Unit Exam Description below and follow directions.

• Section 6.3: Trigonometric Identities
  • Reading: section 6.3
    Read and work through examples 1-8 and their matched problems.
  • The textbook does not talk about how to disprove false identities, but it is very simple. See the supplementary material on disproving identities for a brief discussion.
  • Practice Problems: 6.3 #1, 2, 11, 13, 15, 19, 23, 27, 31, 35, 39, 43, 45, 49, 53, 55, 57, 61, 65, 69, 71, 75, 79, 83, 91, 93, 97, 99, 103
    
    
• Section 6.4: Sum and Difference Formulas
  • Reading: section 6.4
    Read and work through examples 1-10 and their matched problems.
  • Note that the cofunction identities (formulas 3ab) have degree versions as well.
  • Practice Problems: 6.4 #1, 2, 3, 11, 15, 17, 23, 25, 27, 31, 33, 35, 37, 39, 43, 45, 49, 51, 53, 55, 61, 77, 79, 81, 83, 89, 93
    
    
• Section 6.5: Double-Angle and Half-Angle Formulas
  • Reading: section 6.5
    Read and work through examples 1-6 and their matched problems.
  • Practice Problems: 6.5 #7, 11, 15, 19, 21, 23, 29, 35, 39, 43, 47, 51, 53, 55, 57, 59, 61, 75, 83
    
    
• Section 6.6: Product-Sum and Sum-Product Identities
  • Reading: section 6.6
    Read and work through examples 1-2 and their matched problems.
  • Practice Problems: 6.6 #1, 5, 9, 11, 13, 15, 17, 19, 23, 29, 31, 33, 35
    
    
• Supplementary material:
  • Student Solutions Manual
  • For tutoring help, visit the Prentice Hall Tutor Center. Tutors can be contacted by phone, fax, or e-mail. To register, you will need the access code that came with your textbook.
  • Graphing Calculator Help

Unit 5 Pretest and Exam Description

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 6.3
     • Sum, Difference, and Cofunction Identities for sin and cos in section 6.4
     • Double-Angle and Half-Angle Identities for sin and cos in section 6.5
     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:
     • proving identities
     • problems involving the half-angle identities, such as problems #7-18 in section 6.5
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.

Unit 5 Checklist

To finish Unit 5, make sure that you have completed the following items:

• Read the material listed in the Study Guidelines.
• Practice the problems listed in the Study Guidelines, and use any of the listed supplementary material to help you understand the concepts.
• Complete the online Unit Pretest (read the exam description first).
• Complete the online proctored Unit Exam.

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