Table of Contents:

Topics
Study Guidelines
Unit Written Assignment
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 (1.3 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 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 10.1: Polar Coordinates
  • Reading: section 10.1
    Read and work through examples 1-8 and their matched problems.
  • Practice Problems: 10.1 #1-73 odd
  • You can download and print polar graph paper here, or print it from this Polar Graph Paper pdf generator.
    
    
• Section 10.2: Polar Equations and Graphs
  • Reading: section 10.2
    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: 10.2 #1-15 odd, 17-24, 25, 31, 33, 37, 41, 45, 49, 51, 53, 55, 57, 61, 65
  • You can download and print polar graph paper here, or print it from this Polar Graph Paper pdf generator.
    
    
• Section 5.3 (review): Complex Numbers
  • Reading: section 5.3, pages 372-376
    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 #1-20 in this section until you feel comfortable with the concepts listed above.
    
    
• Section 10.3: The Complex Plane; DeMoivre's Theorem
  • Reading: section 10.3
    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: 10.3 #1-49 odd, 51, 53-55
  • You can download and print polar graph paper here, or print it from this Polar Graph Paper pdf generator.
    
    
• 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 6th 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 7 Written Assignment

Be sure to read and follow the 'General Guidelines' (look in Blackboard).