Table of Contents:

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

Topics

In this unit, we study graphs of tangent, cotangent, secant, and cosecant functions, with variations. We also study inverse trigonometric functions. The textbook is quite brief in these sections, so some supplementary material and exercises are included.

• Graphs of variations of tangent, cotangent, secant, and cosecant (7.7)
  • Period and phase shift
• Inverse trigonometric functions: arcsin, arccos, arctan, arcsec (8.1-2)
  • Computations
  • Graphs

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.

• Pages 320-321 (review): Asymptotes
  • Reading: pages 320-321 on vertical and horizontal asymptotes
    
    
• Section 7.7: Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions
  • Reading: section 7.7
    Read and work through examples 1-3 and their matched problems.
  • The textbook neglects any mention of period and phase shift for these four functions. But, just as in section 7.8 for sin and cos, you should be able to determine period and phase shift for variations of these functions. See the supplementary material on period and phase shift for definitions and exercises.
  • You can also try out a java applet that illustrates period, phase shift, and vertical stretching of the graphs of tangent, secant, cotangent, and cosecant.
  • You may of course use your graphing calculator to help graph these functions, but it is also a good idea to be able to do at least a rough sketch by hand. Be sure to take period and phase shift into account when graphing or recognizing graphs of these functions.
  • Practice Problems: 7.7 #1-35 odd
  • Additional exercises on period and phase shift
    
    
• Section 6.1 (review): Inverse functions
  • Reading: section 6.1
  • For a quick review, see the module on inverse functions. This module includes discussion of the concept, examples, and several animations and applets.
  • Practice Problems: Work through a representative sampling of the problems in this section until you feel comfortable with the material.
    
    
• Section 8.1: The Inverse Sine, Cosine, and Tangent Functions
  • Reading: section 8.1
    Read and work through examples 1-8 and their matched problems.
  • This particular book unfortunately uses the sin^-1(x) notation for the inverse trig functions. As noted on page 593, this notation can cause confusion because the -1 exponent is not really an exponent, it's just notation. Therefore, I encourage you to use the more standard notations: arcsin(x), arccos(x), and arctan(x), and I have also used these in the exams. You really should be familiar with both notations.
  • Pay close attention to the definition of the inverse trig functions, particularly the range of these functions:
    • The range of arcsin x is the interval [-pi/2,pi/2].
    • The range of arccos x is the interval [0,pi].
    • The range of arctan x is the interval (-pi/2,pi/2).
  • You may want to print a summary of arcsin(x), arctan(x), and arccos(x).
  • You can also try out a java applet to further explore the definitions of the inverse trig functions.
  • The textbook does not ask any questions involving graphs of the inverse trig functions. Thus, I've installed a practice assignment (on the PHGA testing system) called Practice: Graphs of Inverse Trig Functions to give you some exercises in this area.
  • Practice Problems: 8.1 #1-45 odd, 51
  • Additional practice exercises on graphs of inverse trig functions:
    • At the testing web site, choose Practice: Graphs of Inverse Trig Functions. You may take this as many times as you like - you will see different questions each time.
      
      
• Section 8.2: The Inverse Trigonometric Functions (continued)
  • Reading: section 8.2
    Read and work through examples 1-3 and their matched problems.
  • The arccot and arccsc functions are almost never used. However, arcsec is useful in calculus. Although I have assigned a few exercises involving arcsec, you will not be asked any questions on the exam about these three functions.
  • Practice Problems: 8.2 #1-27 odd, 33, 37, 50
    
    
• Supplementary material (optional):
  • Student Solutions Manual
  • 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 4 Written Assignment

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