Math 141-142: Unit 1

Deadline: Thursday July 18 (141) or Thursday July 11 (142)

Topics
Unit 1 begins with reviews of basic graphing terminology and tools, and then equations and graphs of circles and lines. This is followed by a review of the important concept of a function. Then the trigonometric functions are introduced by first defining and studying the Wrapping Function and then defining the Circular Functions. (This approach defines the trigonometric functions in terms of the unit circle rather than in terms of triangles and angles. The term "trigonometric function" and the connection with triangles and angles will appear in section 5.4.) The unit concludes with a discussion of angles and various ways to measure angles: radians, decimal degrees, and degrees-minutes-seconds.

It is Math Department policy that students should be able to compute the exact values of all the circular (trigonometric) functions at the "standard" angles, i.e., all multiples of pi/6 and pi/4 radians and 30 and 45 degrees. Therefore, no calculators will be allowed on Unit Exam #1. Problems from 5.2 and 5.3 involving calculators will be tested in Unit 2.

• The Wrapping Function (5.1)
• The Circular Functions: sine, cosine, tangent, cotangent, secant, cosecant (5.2)
  • Exact values for particular real numbers
  • Basic properties and identities
• Angles and their Measure (5.3)
  • Radians
  • (Decimal) degrees
  • Degrees-minutes-seconds
  • Conversions between radians and degrees for standard angles (all multiples of pi/6 and pi/4 radians and 30 and 45 degrees)
  • Applications: connection between radians and lengths of arcs

Study guidelines

• Sections 2.1-3 (review): Basic Graphing Tools, Circles, Lines, Functions
  • Reading: pages 98-143.
  • Problems: Work through a representative sampling of the suggested problems in sections 2.1-3 listed below until you feel comfortable with the material.
    • pages 111-115 #1, 3, 7, 11, 15, 19, 21, 23, 27, 29, 31, 33, 35, 37, 39, 49, 51, 55, 57, 65, 69, 75, 77, 83, 87, 91
    • pages 127-131 #1, 3, 7, 11, 15, 17, 19, 21, 23, 25, 29, 35, 37, 41, 43, 45, 51, 53, 59
    • pages 143-147 #1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 43, 47, 49, 51, 53, 55, 87
    • More practice problems, with solutions
      
      
• Section 5-1: The Wrapping Function
  • Reading: pages 340-347.
    Read and work through examples 1-3 and their associated matched problems (1-3).
    Read and respond to "Explore and Discuss" 2.
  • Problems: page 347 #1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 31, 35, 37, 41, 43, 45, 47, 49, 53
    • More practice problems, with solutions
      
      
• Section 5-2: Circular Functions
  • Reading: pages 348-355.
    Read and work through examples 1-3 and their associated matched problems.
    Read and respond to "Explore and Discuss" 1, 2, and 3.
  • Problems: page 355-357 #1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 69, 71, 73, 75, 77, 81, 83, 85
    • More practice problems, with solutions
      
      
• Section 5-3: Angles and Their Measure
  • Reading: pages 357-364.
    Read and work through examples 1-4 and their associated matched problems.
    Read and respond to "Explore and Discuss" 1 and 2.
  • Problems: pages 364-366 #1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 43, 45, 47, 49, 51, 53, 55-66, 67, 71, 73
    • More practice problems, with solutions
      
      
• Supplementary material (optional) for sections 5.1-3:
  • Schaum's Precalculus Outline, chapters 20 and 22
  • Additional application #1, with answer
  • Additional exercises and demonstrations provided by other websites
  • Answers to review problems from the textbook.
  • CD-ROM: 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 #1
After completing the above work, do the following:

1. Before taking Unit Exam #1, you should have completed the Online Testing Practice. If not, then do so now.
2. Read the exam description:
   • This exam has 25 questions, and will count 20 points toward your grade. 
   • This exam has a one hour time limit.
   • It is Math Department policy that students should be able to compute the values of all the circular (trigonometric) functions at the standard angles, i.e., all multiples of pi/6 and pi/4 radians and 30 and 45 degrees. Therefore, calculators will not be allowed on Unit Exam #1. Thus, there will be no problems like #27-32 of section 5.2 or #25-44 of section 5.3 (these will be tested on Unit Exam #2).
   • All of your answers in Unit Exam #1 must be exact. You can type pi for the number pi and sqrt(2) for the square root of 2, etc.
   • Be sure to look under the entry box for the expected format of the answer.
     • Some problems expect an ordered pair, such as (1/2,sqrt(3)/2).
     • None of the problems in this course require answers in terms of units (for example, "5 cm" or "3 ft"). In particular, questions asking for radians or degrees do not expect units (in fact, as noted on page 361, radian measure is a unitless number). Thus, you should not write answers like "pi/4 radians" or "45 degrees". Just write "pi/4" or "45" instead (the problem will tell you if you are supposed to use radians or degress).
3. Complete the online Unit 1 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 1 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.
4. 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.
5. Arrange with your proctor to take the online proctored Unit 1 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 or calculator on this exam.
   • Directions: Click on the link above for your class, then choose Unit 1 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 1 Exam. After the deadline has passed, this exam will be available in practice mode.

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