Math 141-142: Unit 6

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

Table of Contents:

Topics
Study Guidelines
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. (7.7-8)
• Finding approximate solutions of trigonometric equations using a graphical approach. (7.7-8)
• Solving triangles using the Law of Sines (8.2)
• Solving triangles using the Law of Cosines (8.3)
• Applications of the Laws of Sines and Cosines (8.2 & 8.3)
• Formulas for the area of a triangle (8.4)

This is the final unit in the Math 141 course, which concludes with Trigonometry Final Exam.
Math 142 students must also take the Trigonometry Final Exam, and then continue with Units 7, 8, & 9.

Study Guidelines for the 8th edition of Sullivan's Precalculus

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 7.7: Trigonometric Equations (I)
  • Reading: section 7.7
    Read and work through examples 1-6 and their matched problems.
  • Practice Problems: 7.7 #1, 2, 7-51 odds, 66, 67, 71
    
    
• Section 7.8: Trigonometric Equations (II)
  • Reading: section 7.8
    Read and work through examples 1-8 and their matched problems.
  • Practice Problems: 7.8 #1-4, 5, 7, 9, 13, 15, 19, 23, 27, 35, 39, 41, 43, 45, 47, 49, 51, 53, 57, 63, 65, 69
    
    
• Section 8.2: Law of Sines
  • Reading: section 8.2
    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: 8.2 #1, 2, 3, 9, 11, 15, 17, 21-47 odds, 51, 53
    
    
• Section 8.3: Law of Cosines
  • Reading: section 8.3
    Read and work through examples 1-3 and their matched problems.
  • Practice Problems: 8.3 #1, 2, 9, 11, 13, 15, 17, 21, 25, 29, 33-45 odds
    
    
• Section 8.4: The Area of a Triangle
  • Reading: section 8.4
    Read and work through examples 1-2 and their matched problems.
  • Practice Problems: 8.4 #1, 5, 7, 9, 11, 13, 17, 19, 23
    
    
• Supplementary material:
  • Student Solutions Manual
  • 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 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.
   • Many questions on this exam ask for an exact answer. You should not try to use a calculator approximation for these questions.
   • 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 #9 in section 8.2, just enter 5*sin(45)/sin(95) in your calculator (i.e., don't roundoff sin(45) and sin(95) and then divide).
   • 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.
   • 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 in section 7.3
     • Sum, Difference, and Cofunction Identities for sin and cos in section 7.4
     • Double-Angle and Half-Angle Identities for sin and cos in section 7.5
     • Law of Sines and Law of Cosines in sections 8.2-8.3
     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 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 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 due date.
     Your best score counts, and it will be rescaled to 5 points maximum.
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. Arrange with your proctor to take the online proctored Unit 6 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 on this exam.
   • Directions: Click on the link above for your class, then 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 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 6 Practice Exam. After the deadline has passed, this exam will be available in practice mode.

Unit 6 Checklist

To finish Unit 6, make sure that you have completed the following items:

• 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 online Unit Pretest (read the exam description first).
• Complete the online proctored Unit Exam.

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