Math 25: Unit 2

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

Table of Contents:

Topics
Study Guidelines

Topics
The first part of Unit 2 continues the development of the trigonometric functions by studying their value at general angles. In section 7.4, these values are computed by using the reference triangle technique. In section 7.5, an alternative approach, using the unit circle, is given. In fact, this actually provides a second alternative definition of the trigonometric functions. It is very important that you learn both approaches to the definition and calculation of trigonometric functions.

In the second part of Unit 2, you will see how trigonometry can be used to solve a large variety of applications involving right triangles.

• Reference angles (7.4)
  • Sign of trig functions in different quadrants
• Unit circle approach to the definition of trig functions (7.5)
  • Properties of trig functions
• Applications involving right triangles (9.1)

Study guidelines for the 8th 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 graded carefully, you will probably not do well in the course if you do not complete these and check your work as described above.

• Section 7.4: Trigonometric Functions of General Angles
  
  • Reading: section 7.4
    Read and work through examples 1-8 and their matched problems.
    You should become familiar with the signs of the various trig functions in the four quadrants (this is actually easier to remember after you have covered section 7.5).
    You should also become adept at using reference angles to compute the values of the trig functions at a general angle.
  • Practice Problems: 7.4 #11-19 odds, 21, 25, 31, 33-39 odds, 41, 45, 47, 49, 51, 57, 59, 61, 67, 69, 71, 75, 77, 81, 83, 87, 89, 91, 95, 97, 99, 101, 105, 107, 109, 111, 113, 115, 117
    
    
• Section 7.5: The Unit Circle Definition of the Trigonometric Functions
  
  • Reading: section 7.5
    Read and work through examples 1-3 and their matched problems.
    This is a very important section. The trigonometric functions are defined a second time in this section, this time in terms of the unit circle. This makes it easy to see that each trigonometric function is actually a function whose domain is the set of real numbers. It is crucial that you do not get locked into thinking of trigonometric functions just in terms of triangles. Although the original definition is easy for acute angles, this second definition is easier to use for general angles.
  • You can download a copy of the unit circle with the values of sin and cos for the standard angles.
  • Practice Problems: 7.5 #9-19 odds, 21, 27, 33, 35, 37, 41, 45, 51, 55, 57, 59, 61-87 odd, 91-99 odd
    
    
• Sections 7.3 and 9.1: Applications Involving Right Triangles
  
  • One of the primary uses of trigonometry is to solve problems involving right triangles. In this section, a variety of such applications are demonstrated.
    
  • Reading: section 7.3
    Read and work through examples 7-9 and their matched problems.
    
  • Practice Problems: 7.3 #51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71.
    
  • Reading: section 9.1
    Read and work through example 1 and its matched problem. Skip the other examples for now.
    
  • Practice Problems: 9.1 #9, 11, 13, 15, 17, 27ab, 31, 33.
    
    

• 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

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