Math 141-142: Unit 3

Note: The information on this page is for the 8th edition of the textbook.
Click here for the 7th edition information.
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 study the basic properties of the graphs of the sine and cosine functions, with variations. These functions can be used to study harmonic motion.

• Review of graphing: x-intercepts, y-intercepts, domain, range, axes, increasing and decreasing intervals, asymptotes. (1.2 and 2.5)
• Graphs of the sine and cosine functions. (6.4 and 6.6)
  • Period, amplitude, and phase shift
• Simple harmonic motion (8.5)

Study Guidelines for the 8th 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.

• Sections 1.2 and 2.5 (review): Graphing
  • Reading: sections 1.2 and 2.5
    Concepts you should know:
    • x-intercepts, y-intercepts, axes
    • domain, range
    • increasing and decreasing intervals
    • vertical translation
    • horizontal translation
    • reflection
    • vertical compression and stretching
    • horizontal compression and stretching
      
      
• Section 6.4: Graphs of the Sine and Cosine Functions
  • Reading: section 6.4
    Read and work through examples 1-9 and their matched problems.
  • You can view an animation which illustrates how the sine curve is created.
  • Practice Problems: 6.4 #1, 2, 9-41 odds, 45, 47, 51, 53, 59, 65, 67-83, 91, 93, 95
    
    
• Section 6.6: Phase Shift; Sinusoidal Curve Fitting
  • Reading: section 6.6
    Read and work through examples 1-2 and their matched problems.
    You will not be required to find sinusoidal functions from data points, as in examples 3-5. However, it is a useful calculator skill, so I recommend that you read examples 3-5 and try problem 29 and 35..
  • Try out a java applet that illustrates the various aspects of harmonic motion: amplitude, period, and phaseshift.
  • Practice Problems: 6.6 #3-25 odds, 29, 35
    
    
• Section 8.5: Simple Harmonic Motion; Damped Motion; Combining Waves
  • Reading: section 8.5
    Read and work through examples 1-2 and their matched problems.
    You will only be required to answer questions about simple harmonic motion, as in problems 5-20. Nevertheless, you should also read the section on Damped Motion (including example 3) and try problems 21 and 23.
  • You can view an animation which illustrates how the motion of a spring generates a cosine curve.
  • Practice Problems: 8.5 #1, 5-23 odds
    • Additional spring problems #1-4 (solutions are included)
      
      
• 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 3 Pretest and Exam Description

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 #71-84 of section 6.4). 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 Practice Exam. After the deadline has passed, this exam will be available in practice mode.

Unit 3 Checklist

To finish Unit 3, 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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