Math 25: Unit 6

Target Date: Thursday November 2
Deadline: Friday November 3

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

Table of Contents:

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

Topics

This unit consists of two parts. The first part finishes the study of trigonometric identities begun in Unit 5. In this section you will use the various trigonometric identities to help solve equations involving trigonometric functions.The second part is a study of methods for solving general triangles, using the Law of Sines and the Law of Cosines. Included are many different applications, along with a short section on two new formulas for the area of a triangle.

• Finding exact and/or approximate solutions to trigonometric equations using an algebraic approach. (8.7-8)
• Finding approximate solutions of trigonometric equations using a graphical approach. (8.7-8)
• Solving triangles using the Law of Sines (9.2)
• Solving triangles using the Law of Cosines (9.3)
• Applications of the Laws of Sines and Cosines (9.2 & 9.3)
• Formulas for the area of a triangle (9.4)

Unit 6 will be followed by the Trigonometry Final Exam.

Study guidelines for the 6th 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 8.7: Trigonometric Equations (I)
  • Reading: section 8.7
    Read and work through examples 1-6 and their matched problems.
  • Practice Problems: 8.7 #1-43 odd, 47
    
    
• Section 8.8: Trigonometric Equations (II)
  • Reading: section 8.8
    Read and work through examples 1-8 and their matched problems.
  • Practice Problems: 8.8 #1, 3, 5, 9, 11, 15, 19, 23, 27, 31, 33, 35, 37, 41, 43, 45, 49, 55, 57, 61
    
    
• Section 9.2: Law of Sines
  • Reading: section 9.2
    Read and work through examples 1-7 and their matched problems.
  • Try out the Law of Sines SSA applet. You can experiment with the construction to see how to get 0, 1, or 2 solutions in the SSA case.
  • Practice Problems: 9.2 #1, 3, 7, 9, 13-37 odd, 41, 43
    
    
• Section 9.3: Law of Cosines
  • Reading: section 9.3
    Read and work through examples 1-3 and their matched problems.
  • Practice Problems: 9.3 #1, 3, 5, 7, 9, 13, 17, 21, 25-39 odd
    
    
• Section 9.4: The Area of a Triangle
  • Reading: section 9.4
    Read and work through examples 1-2 and their matched problems.
  • Practice Problems: 9.4 #1, 3, 5, 7, 9, 13, 17, 21
    
    
• 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.
  • 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 first obtain an access code from me.
  • Graphing Calculator Help

Unit 6 Written Assignment

Complete the following problems by Thursday November 2:

• View or print this handout with the detailed assignment
  (pdf format - you will need a copy of Acrobat Reader to view and print the file)

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 6 Pretest and Exam Description

After completing the above work, do the following:

1. Read the exam description:
   • This exam has 16 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 (for example, solutions of equations) expect a list of several values or formulas separated by semicolons, such as 0;5pi/6;7pi/6. In this case, the order of the values is not important.
   • Many questions on this exam ask for an exact answer. You should not try to use a calculator approximation for these questions. 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 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.
   • Very important: When solving triangles using the law of sines or the law of cosines, be sure to retain as much accuracy as possible in your calculations. If you round off intermediate results, you can get very inaccurate answers. For example, to find b in problem #1 in section 9.2, just enter 5*sin(45)/sin(95) in your calculator (i.e., don't roundoff sin(45) and sin(95) and then divide).
   • Make sure your calculator is set to the correct mode (radians or degrees) for each problem.
   • For this exam, you must know how to find intersections of curves using your calculator.
   • You will need to memorize the following formulas:
     • Basic identities (page 583 in section 8.3)
     • Sum, difference, and cofunction identities for sin and cos (formulas 1-5 in section 8.4)
     • Double-angle and half-angle identities for sin and cos (formulas 1-4, 6, 7, 10ab in section 8.5)
     • Law of Sines and Law of Cosines in sections 9.2-9.3
     • Area formulas in section 9.4
     You will not need to use any of the other trigonometric identities on this exam, so you will not be given any formula sheet to use on this exam.
   • In previous classes, students had the most difficulty trying to solve trigonometric equations.
2. Complete the online Unit 6 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 6 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 6 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 6 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 6 Practice Exam. After the deadline has passed, this exam will be available in practice mode.

Unit 6 Checklist

Make sure that you have finished the following items to complete Unit 6:

• 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 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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