Math 142: Unit 7

Target Date:Monday April 14
Deadline: Friday April 18

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

The Analytic Geometry section of the course begins with this unit, which consists of two parts. The first is an introduction to polar coordinates for points in the xy-plane, and polar equations and their graphs. The second is a study of complex numbers. The two topics are related by the polar form of a complex number, which then leads to simple formulas for finding powers and roots of complex number via DeMoivre's Theorem.

• Polar Coordinates (9.1-2)
  • Converting from rectangular to polar coordinates
  • Converting from polar to rectangular coordinates
  • Equations in polar coordinates
  • Graphs of functions and relations given in polar coordinates
• Complex numbers (A.7 and 9.3)
  • Definition
  • Addition and subtraction
  • Multiplication
  • Division
  • Polar form
• DeMoivre's Theorem (9.3)
  • Powers of complex numbers
  • Roots of complex numbers

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 9.1: Polar Coordinates
  • Reading: section 9.1
    Read and work through examples 1-8 and their matched problems.
  • Practice Problems: 9.1 #1-4, 11-83 odds, 84
  • You can download and print polar graph paper.
    
    
• Section 9.2: Polar Equations and Graphs
  • Reading: section 9.2
    Read and work through examples 1-13 and their matched problems.
  • Many of the polar graphs (for example, the roses) are similar to the pictures that can obtained by using a spirograph. Note that we can always rewrite any polar equation r=f(t) as a set of parametric equations x=f(t)*cos(t), y=f(t)*sin(t). In a similar way, spirograph pictures are obtained by using certain parametric equations involving trigonometric functions. For the details, see Anu Garg's wonderful spirograph applet.
  • Practice Problems: 9.2 #1-6, 13-27 odds, 29-36, 37, 43, 45, 49, 53, 57, 61-64, 65, 67, 69, 71, 73, 77, 81
  • You can download and print polar graph paper.
    
    
• Section A.7 (review): Complex Numbers
  • Reading: section A.7, pages A54-A58
    Concepts you should know:
    • definition of complex numbers
    • addition and substraction of complex numbers
    • multiplication of complex numbers
    • division of complex numbers
  • Practice Problems: Work through a representative sampling of problems #9-46 in this section until you feel comfortable with the concepts listed above.
    
    
• Section 9.3: The Complex Plane; DeMoivre's Theorem
  • Reading: section 9.3
    Read and work through examples 1-6 and their matched problems.
  • The following applets illustrate the geometric distribution of the n complex nth roots of a complex number:
    • complex square roots
    • complex cube roots
    • complex 4th roots
    • complex 5th roots
  • Practice Problems: 9.3 #1-4, 11-59 odds, 61, 63-65
  • You can download and print polar graph paper.
    
    
• 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 7 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.
   • All questions on this exam require an exact answer. You should not try to use a calculator approximation for any of these questions.
   • Type the letter i for the square root of -1, and the letter e for the number e. Be careful to put in all necessary parentheses when typing your answer, especially for problems in polar form. For example, 1+i in polar form would be entered as sqrt(2)*(cos(pi/4)+i*sin(pi/4)). Make sure you use the preview button to prevent any mistakes! (The second form above looks better in the preview, but both are correct.)
   • Be sure to look under the entry box for the type of answer expected.
     • Some problems 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.
     • The answer to some problems is an equation (for example, the equation of a line). In this case, simply type in the equation. For example, your answer might be y=2x-3 or r=cos(t).
   • Make sure your calculator is set to the correct mode (radians or degrees) for each problem.
   • For this exam, you must know how to graph curves in polar coordinates using your calculator.
   • This exam may be somewhat easier if you know how to work with complex numbers on your calculator. However, remember that you should not use approximations -- all questions on this exam require an exact answer.
   • In previous classes, students had the most difficulty with (a) finding roots of complex numbers and (b) converting from rectangular to polar coordinates (or rectangular to polar form of a complex number).
2. Complete the online Unit 7 Pretest assignment for 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 7 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 7 Exam assignment for 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 7 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 142 for specific rules.

   Note: Remember that you can always go back and take practice exams on this unit for 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 7 Practice Exam. After the deadline has passed, this exam will be available in practice mode.

Unit 7 Checklist

To finish Unit 7, 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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