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

Table of Contents:

Topics
Study Guidelines

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.

• 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, we encourage you to use the more standard notations: arcsin(x), arccos(x), and arctan(x), and we use 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, so you should make good use of the "Practice" assignments in Optimath that involve graphs of the inverse trigonometric functions.
  • Practice Problems: 8.1 #1-45 odd, 51