Topics
Unit 1 begins with a discussion of angles and various ways to measure angles: radians, decimal degrees, and degrees-minutes-seconds. Then the trigonometric functions are defined in terms of the unit circle, rather than in terms of right triangles (which you may have seen before). The connection with right triangles will appear in Unit 2.

It is Math Department policy that students should be able to compute the exact values of all the 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 5.1-3 involving calculators will be tested in Unit 2.

• Angles and their Measure (5.1)
  • 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)
• The Trigonometric Functions: sine, cosine, tangent, cotangent, secant, cosecant (5.2-3)
  • Exact values for particular real numbers (angles)
  • Evaluation of trigonometric functions using a circle
  • Basic properties and identities
  • Solving "inverse" problems: given the value of a trig function, what is the corresponding angle?

Study guidelines

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 5-1: Angles and Their Measure
  • Reading: section 5.1, pages 304-310
    Read and work through examples 1-5 and their corresponding matched problems.
  • Problems that require calculators will be tested in Unit 2.
  • Problems involving arc length, areas of sectors, and circular motion will also be tested in Unit 2.
  • Practice Problems: 5.1 #1-35 odd
• Section 5-2: Trigonometric Functions: Unit Circle Approach
  • Reading: section 5.2, pages 317-328, 329-330
    Read and work through examples 1-10 and example 12 and their corresponding matched problems.
  • Problems that require calculators will be tested in Unit 2.
  • You can download a copy of the unit circle with the values of sin and cos for the standard angles.
  • Practice Problems: 5.2 #1-55 odd, 73-101 odd
    
    
• Section 5-3: Properties of the Trigonometric Functions
  • Reading: section 5.3
    Read and work through examples 1-7 and their corresponding matched problems.
  • Practice Problems: 5.3 #1-47 odd, 49, 53, 57, 61, 65, 69, 73, 77, 81, 83
    
    
• Supplementary material for sections 5.1-3:
  • 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 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 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, for example, there will be no problems like #57-80 of section 5.1 or #57-72 of section 5.2 (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.

back to the self-paced Math 141-142 home page