Math 25: Unit 1

Target Date: Thursday September 3
Deadline: Wednesday September 9

Note: The information on this page is for the 7th edition of the textbook.
Click here for the 8th edition information.
Click here for the 6th edition information.

Table of Contents:

Topics
Study Guidelines
Unit Written Assignment
Unit Pretest
Unit Exam Description
Unit Exam
Checklist

Topics
Unit 1 begins with a discussion of angles and various ways to measure angles: radians, decimal degrees, and degrees-minutes-seconds.You are probably familiar with degrees, but in mathematics it is more convenient to use radians. You will also learn to convert between the three measurements.

The six trigonometric functions are then defined in terms of right triangles (in Unit 2, you will learn a second approach to the definition in terms of the unit circle). You will also learn how to compute the exact values of these functions at certain angles, and approximations at more general angles. 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.

Finally, you will also learn some of the basic identities that are satisfied by the trigonometric functions.

• Angles and their Measure (6.1)
  • 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)
  • Conversions between radians, (decimal) degrees, and degrees-minutes-seconds for general angles
  • Applications:
    • connection between radians and lengths of arcs
    • areas of sectors of circles
    • circular motion
• Definition of trigonometric functions in terms of right triangles (6.2)
• Fundamental identities of trigonometric functions (6.2)
• Exact evaluation of trigonometric functions at standard acute angles (0, pi/6, pi/4, pi/3, and pi/2) (6.3)
• Approximate evaluation of trigonometric functions with a calculator (make sure your calculator is set to the correct mode!) (6.3)

Study guidelines for the 7th edition of Sullivan's Algebra and Trigonometry

These reading and problem assignments are designed to help you learn the course material. After completing these Study Guidelines, complete the Unit 1 Written Assignment, and then complete the Unit 1 Pretest and the Unit 1 Exam.

In each textbook section, you should:

1. Read the indicated material.
2. Complete the Practice Problems. Check the odd-numbered answers in the textbook. If you miss any of these problems, try them again before consulting the solutions. Go back to the section text and reread relevant material and examples if necessary. If the problem is again incorrect, then you can check the Solutions Manual. Be sure to get help if you need it.
   • 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.
3. Be sure to read and respond to the discussions on myCR. If you have a question, post it myCR and check regularly for a response.
   • Note: If you subscribe to the discussion forum that corresponds to this unit, then forum posts will also show up in your email.
4. Complete the portion of the Unit 2 Written Assignment that covers this section.
   • Note that the written assignment is due on the Target date, not the Deadline date.

Note: Recommended starting dates for each section are provided below, on a Tuesday-Thursday schedule. However, note that sometimes you may need to cover two sections during the same time period. See the course calendar for a visual display of recommended starting dates.

• Section 6.1: Angles and Their Measure
  (Aug. 26)
  • Reading: section 6.1
    Read and work through examples 1-8 and their matched problems.
    You should know the relationships between arc length and radians and between degrees and radians. Also, you should become very familiar with the "standard" angles given in Table 1.
  • Practice Problems: 6.1 #11, 13, 17, 19, 23-33 odd, 35, 37, 41, 43, 47, 49, 53, 55, 59-69 odd, 71, 73, 79, 81, 87, 91, 92, 95, 97, 99, 101, 103, 105, 107, 109
  • Additional examples and exercises on circular motion
    
    
• Section 6.2: Right Angle Trigonometry
  (Aug. 28)
  • Reading: 6.2
    Read and work through examples 1-7 and their matched problems.
    You should know identities (1)-(7).
  • Practice Problems: 6.2 #11-35 odd, 37, 39, 43, 45, 51, 53, 55, 57, 65, 67, 69
    
    
• Section 6.3: Computing the Values of Trigonometric Functions of Given Angles
  (Sept. 2)
  • Reading: 6.3
    Read and work through examples 1-6 and their matched problems.
    You should know the values of all of the trig functions at the standard angles listed in Table 3.
  • Practice Problems: 6.3 #7-29 odd, 31, 35, 39, 43, 45, 49, 51, 55
    
    

• Student Solutions Manual
• Algebra Review booklet
• CD lecture series for the 7th edition (step-by-step video examples on CD)
• Video lectures are available on reserve in the CR library.
  • Section numbering on the video lectures corresponds to the 7th edition of the textbook. Use the section correlation guide to find the corresponding sections for the 6th edition.
• For tutoring help, visit the online tutoring.
  
• Online Practice Exercises
• Graphing Calculator Help

Unit 1 Written Assignment

Complete the following two problems by Thursday September 3:

• 7th edition: 6.1 #102 and #106

Be sure to read and follow the Homework Guidelines.
Post a question on myCR if you are unsure of how to begin one of the problems.

Consult the Distance Education page for instructions on how to turn in your assignment.

Unit 1 Pretest

1. Before taking the Unit 1 Pretest, you should have completed the Online Testing Practice. If not, then do so now.
2. Read the exam description:
   • Many of the questions expect an exact answer. You can type pi for the number pi and sqrt(2) for the square root of 2, etc.
   • Other questions on this exam ask for an approximation instead of an exact answer. These questions will ask you to give an answer "with an accuracy of at least two decimal places after the decimal point" (or possibly one decimal, or three decimals, etc.). In this case, you would have to enter at least two digits after the decimal point. For example, if you calculate your answer to be 1.41421356237, then you could enter 1.41, 1.414, 1.4142, etc. When you view your corrected exam, you will see that the "correct" answer is 1.41421356237. However, any response within 0.01 of this number counts as correct.
     • Note: If a question does not ask for an approximation, then your answer must be exact.
   • 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).
     • Some problems expect a list, separated by commas, such as 1/2,sqrt(3)/2,sqrt(3). The values must be listed in the order requested in the problem.
     • None of the problems in this course require answers in terms of units, or dimensions (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 481, radian measure is a dimensionless 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 degrees).
   • If an angle measure doesn't say "degrees" or use the degree symbol, then it is in radians.
   • Make sure your calculator is set to the correct mode (radians or degrees) for each question.
3. This pretest has 25 questions, and a one hour time limit. It will count 5 points toward your grade. 
4. Complete the online Unit 1 Pretest assignment (see the instructions for pretests).
   • Directions: At the testing web site, choose Unit 1 Pretest.
   • You may use your book and notes if you wish.
   • 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 deadline date.
   • Your highest pretest score will count, and will then be rescaled to 5 points maximum.
5. If you are having trouble with any of the problems listed above on the pretest, make use of the help resources listed on the Help page.

Unit 1 Exam

1. Read the exam description above.
2. This exam has 25 questions, and a one hour time limit. It will count 20 points toward your grade.
3. Make arrangements with your proctor to take the online proctored Unit 1 Exam assignment (see the instructions for proctored exams).
   • Directions: At the testing web site, choose Unit 1 Exam.
   • Remember to bring identification to the testing location.
   • You may NOT use your book or notes on this 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 instructions for proctored exams for specific rules.
   • Your highest exam score will count, and will then be rescaled to 20 points maximum.

Note: Remember that you can always go back and take practice exams on this unit after the deadline has passed. In particular, this will help you prepare for the midterm and final exams.

• Directions: At the testing web site, choose Unit 1 Practice. After the Unit deadline has passed, this practice exam will become available.

Unit 1 Checklist

Make sure that you have finished the following items to complete Unit 1:

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

Distance Education students: Remember to check in with the instructor via email or phone, and participate in the online discussion forums on myCR.

Math 25 home page