Math 141-142: Unit 3

Deadline: Thursday August 1 (141) or Thursday July 25 (142)

Topics

In this unit you will study the basic properties of the graphs of the six trigonometric functions, and you will study the graphs of sine and cosine, with variations, in much more detail.

• Review of graphing: x-intercepts, y-intercepts, domain, range, axes, increasing and decreasing intervals, asymptotes. (2.4, 2.5, and 3.4)
• Periodic functions; graphs of the six trigonometric functions. (5.6)
• Simple harmonic motion: graphs of variations of sine and cosine. (5.7)
• Period, amplitude, phase shift, vertical translation. (5.7)

Study guidelines

• Sections 2.4, 2.5, and 3.4 (review): Graphing functions
  • Reading: pages 147-177, and also material on vertical and horizontal asymptotes on pages 251-254.
    Concepts you should know:
    • x-intercepts, y-intercepts, axes
    • domain, range
    • increasing and decreasing intervals
    • vertical and horizontal asymptotes
    • vertical translation
    • horizontal translation
    • reflection
    • vertical expansion and contraction
  • Problems: Work through a representative sampling of the suggested problems in sections 2.4-2.5 listed below until you feel comfortable with the material.
    • pages 161-165: #1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 31, 33, 37, 51, 53, 63, 75, 77, 81, 87
    • pages 177-181: #1, 3, 7, 9, 11, 13, 15, 17, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 47, 49, 51, 59, 75, 79, 85, 87, 89
  • More practice problems, with solutions
    
    
• Section 5.6: Graphing Basic Trigonometric Functions
  • Reading: pages 391-401.
    Read and work through examples 1 and 2 and their associated matched problems.
    Read and respond to "Explore and Discuss" 1 and 2.
    If you need help with your TI calculator, you can try the Graphing Calculator Workshop.
  • Problems: pages 401-402  #1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 25, 27, 29
  • More practice problems, with solutions
    
    
• Section 5.7: Graphing y=k+A sin(Bx+C) and y=k+A cos(Bx+C)
  • Reading: pages 403-414.
    Read and work through examples 1-8 and their associated matched problems.
  • Problems: pages 415-419: #1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 61, 63, 65, 71, 73
    • Additional spring problems #1-4 (solutions are included)
  • More practice problems, with solutions
    
    
• Supplementary material (optional)
  • Schaum's Precalculus Outline, chapter 21
  • Additional application #3 for chapter 5, with answer
  • Additional exercises and demonstrations provided by other websites, for chapter 2, chapter 3, or chapter 5.
  • Answers to review problems from the textbook.
  • Calculator key stroke guides
  • The CD-ROM that came with your textbook has tutorials, practice exams, and interesting "Interactive Diagrams".
  • Browse through the Archive Center on the NetTutor web site (see the Online Tutoring page for instructions on how to get started with NetTutor). Detailed solutions to selected problems are saved in the Archive Center.

Unit Exam #3

After completing the above work, do the following:

1. Read the exam description:
   • This exam has 20 questions, and will count 20 points toward your grade. 
   • This exam has a one hour time limit.
   • Be sure to look under the entry box for the type of answer expected.
     • Some problems ask you for the formula (i.e., function) which corresponds to a given graph (similar to problems #21-28 of section 5.7). Your answer should be something like 4*sin(3x). Do not put y= in front. Also, make sure that you put in enough parentheses in your answers, and put them in the correct places. For example, the answer 4*sin(3)x would not be the same as 4*sin(3x).
     • 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 something like 1/2,sqrt(3)/2,sqrt(3).
   • Make sure your calculator is set to the correct mode (radians or degrees) for each problem.
   • This exam will be much easier if you are good at using the graphing features of your calculator. However, it will slow you down if you depend too much on your calculator. Be sure to consider basic properties such as periods, amplitudes, and phase shifts when you are dealing with questions about graphs.
2. Complete the online Unit 3 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 3 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 3 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 3 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 3 Exam. After the deadline has passed, this exam will be available in practice mode.

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