Math 25: Unit 2

Target Date: Tuesday September 19
Deadline: Friday September 22

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

Table of Contents:

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

Topics
The first part of Unit 2 continues the development of the trigonometric functions by studying their value at general angles. In section 6.4, these values are computed by using the reference triangle technique. In section 6.5, an alternative approach, using the unit circle, is given. In fact, this actually provides a second alternative definition of the trigonometric functions. It is very important that you learn both approaches to the definition and calculation of trigonometric functions.

In the second part of Unit 2, you will see how trigonometry can be used to solve a large variety of applications involving right triangles.

• Reference angles (6.4)
  • Sign of trig functions in different quadrants
• Unit circle approach to the definition of trig functions (6.5)
  • Properties of trig functions
• Applications involving right triangles (8.1)

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. 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 6.4: Trigonometric Functions of General Angles
  • Reading: section 6.4
    Read and work through examples 1-8 and their matched problems.
    You should become familiar with the signs of the various trig functions in the four quadrants (this is actually easier to remember after you have covered section 7.5).
    You should also become adept at using reference angles to compute the values of the trig functions at a general angle.
  • Practice Problems: 6.4 #11-19 odd, 21, 25, 31, 33-39 odd, 41, 45, 47, 49, 51, 57, 59, 61, 67, 69, 71, 75, 77, 81, 83, 87, 89, 91, 95, 97, 99, 101, 105, 107, 109, 111, 113, 115, 117
    
    
• Section 6.5: The Unit Circle Definition of the Trigonometric Functions
  • Reading: section 6.5
    Read and work through examples 1-3 and their matched problems.
    This is a very important section. The trigonometric functions are defined a second time in this section, this time in terms of the unit circle. This makes it easy to see that each trigonometric function is actually a function whose domain is the set of real numbers. It is crucial that you do not get locked into thinking of trigonometric functions just in terms of triangles. Although the original definition is easy for acute angles, this second definition is easier to use for general angles.
  • You can download a copy of the unit circle with the values of sin and cos for the standard angles.
  • Practice Problems: 6.5 #9-19 odd, 21, 27, 33, 35, 37, 41, 45, 51, 55, 57, 59, 61-97 odd
    
    
• Section 8.1: Applications Involving Right Triangles
  • Reading: section 8.1
    Read and work through examples 1-9 and their matched problems.
    One of the primary uses of trigonometry is to solve problems involving right triangles. In this section, a wide variety of such applications are demonstrated.
  • Practice Problems: 8.1 #9, 13, 17, 19, 23-35 odd, 39, 41, 43, 53
    
    
• Supplementary material (optional):
  • Student Solutions Manual
  • Algebra Review booklet
  • CD lecture series (step-by-step video examples on CD)
    • Section numbering on the CD's corresponds to the 7th edition of the textbook.Use the section correlation guide to find the corresponding sections for the 6th edition.
  • 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 Prentice Hall Math Tutor Center. Tutors can be contacted by phone, fax, or e-mail. To register, you will need to use your access code.
  • Graphing Calculator Help

Unit 2 Written Assignment

Complete the following problems by Tuesday September 19:

• 7th edition: 8.1 #32, 36

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

Unit 2 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.
   • 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 decimals 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  0.01. The symbol means "plus or minus", so anything within 0.01 of the first number counts as correct.
     • 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.
2. Complete the online Unit 2 Pretest assignment. 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: At the testing web site, choose the Unit 2 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 deadline date. Your best score counts, and it will be rescaled to 5 points maximum.
   • See the instructions for pretests.
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. Go to the Academic Support Center to take the online proctored Unit 2 Exam assignment (see the instructions for proctored exams). 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: At the testing web site, choose Unit 2 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 specific rules.

   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 2 Practice Exam. After the deadline has passed, this exam will be available in practice mode.

Unit 2 Checklist

Make sure that you have finished the following items to complete Unit 2:

• 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 each week with the instructor, and participate in the online discussion forums on Blackboard.

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