Last Updated: 9:30PM on 1/28/11

Math 95 Page Contents

• Textbook Info
• Homework Assignments 
• Links of Interest
• Mathematica Player and Interactive Notebooks
• Other Useful Software

Textbook Info

• Trigonometry: A Unit Circle Approach, by Michael Sullivan (Custom Edition for City College of San Francisco).

Students are highly encouraged to look over the material in Chapter 1 as well as the several appendices A1-A8 at the end of the book. Looking through this material may prompt you to review various topics with which you may be "rusty"... or at the very least make you are aware of where to locate review info if you need to revisit it later in the course. Though this material may not be fresh in your mind, most of it should be familiar, and you should be able to review it and get up to speed fairly quickly for this course. If that's not the case, you should likely be enrolling in Math 90 (Advanced Algebra) rather than Math 95.

Please note that homework will be assigned in class whenever we begin a new section of the text. All the HW assigned in any given week will generally be collected on the first class meeting of the following week. I'll regularly update this HW assignments below, as we proceed through the semester.

Note Concerning Access to "CourseCompass" Web Resources: The "CourseCompass" web resources are packaged with some new copies of our course textbook. Note that use of the CourseCompass software is NOT required in this section of Math 95. But it is being made available as an option for those who want to use it. If you'd like to access these materials (and you purchased the necessary "code number" when you bought your copy of the textbook at the bookstore) visit the publishers webpage "How to Register", where you'll be led through their (Pearson Publishers) registration process. When asked for a "Course ID" use "ccsf47948".

Homework Assignments

• § 2.1: #1-10 all, 11-23 odd, 29, 35-59 odd, 67, 71-77 odd, 87, 89, 99, 101, 103, 107, 114.

HW Packet 1: The assignment for the first week of class is to read §2.1 and write up solutions to the homework assigned from §2.1 above. This will be due on Monday, Jan. 24.

Some students spoke with me on Friday indicating they'de already finished the assignment. If you do finish early, and would like to work ahead, you can begin reading the paper (PDF) by Phillipe Laval referred to below.

• "Right Triangle Approach": Before we begin §2.2 of our textbook, we'll discuss some preliminary material in class, such as similar triangles, the Pythagorean Theorem, and most importantly... the "Right-Triangle Approach" to defining the six trigonometric functions. The main ideas we'll focus on are summarized in this week's class handouts (listed below).

  For two alternate discussions of the Right Triangle Approach to trigonometry, you can visit this web page by David Joyce, and study pages 13-18 of the well-written document Trigonometric Functions and Triangles, by Phillipe B. Laval (available as a PDF file at this link). Note that the first 10 pages of Laval's paper overlap with material from §2.1 of our text, but also introduce the useful concept of "reference angles" (on pages 6-7).

  HW Packet 2: Due on Monday, Jan. 31: The exercises at the end of the handouts (listed below) distributed in class this week:

  • "Right Triangle Trig: Basic Definitions" (PDF here [120KB]);
  • "Right Triangle Approach to Trig: Summary & Exercises";
  • "Using Right Triangles to Tabulate Sine and Cosine Values" (PDF here [68 KB]).
• § 2.2: #1, 9, 10, 11-31 odd, 39, 41, 49, 53, 55, 59, 63, 83, 85, 97, 99. [Note: Look here for a "Unit Circle Diagram" link which may be helpful for this HW assignment...and in the future. ]
• § 2.3: #1-11 all, 17-37 odd, 43, 45, 49, 51, 53, 55, 59, 69, 93, 113.

For Monday, February 14: The assignment from §2.3, and the exercises from the two class handouts (given out on Wed and Fri) will be collected. We will wrap up §2.3 and begin discussing graphs of trigonometric functions in class on Monday, 2/14.

• Posted 2/15/11: A copy of the exercise handout from last Friday (with the answers filled in) can be viewed by clicking this link: "Visualizing Trig Function Values: Unit Circle, Tangent, and Cotanget Lines".
• Note: As part of this weeks homework, please read the section lower on this web page on Mathematica Player and Interactive Notebooks. Download and install the Mathematica Player program, and use it to view the interactive Mathematica notebook file described in that section below (i.e. "3_TrianglesIn1stQuad.nbp").
• § 2.4: #3, 6, 8, 9, 11, 15-23 odd, 29-37 odd, 43-51 odd, 55, 61, 67-75 odd, 79.
• § 2.5: #3-6 all, 11-17 odd, 18, 21-35 odd.
• § 2.6: #1, 3, 5, 11, 15-27 odd, 33, 35.
• § 3.1: #1-12 all, 13-23 odd, 27, 29, 37-47 odd, 55, 57, 61, 63, 65.
• § 3.2: #1-8 all, 9-25 every other odd, 37-47 every other odd, 57-73 odd.
• § 3.3: #1-8 all, 9-19 odd, 23, 27, 33, 35, 49, 53, 69, 71, 91, 104.
• § 3.4: #1-8 all, 9, 11, 15, 21, 23, 25, 31, 33, 37-43 odd, 46, 55, 57, 71, 77, 83, 87.
• § 3.5: #1-6 all, 7, 11, 13, 17, 29, 31, 33, 47, 69, 71, 73, 77.
• § 3.6: #1, 3, 5, 11, 13, 15, 17.
• § 3.7: #1-6 all, 7-15 odd, 33, 35, 37, 53.

HW Due Monday, May 2: Homework assigned from §3.6—§3.7 above.

• § 3.8: #1-3 all, 5, 7, 11, 15, 23, 25, 41, 65.
• § 4.1: #1-8 all, 9, 15, 29, 31, 37, 41, 49, 51, 57, 69.
• § 4.2: #1-8 all, 9, 11, 13, 39, 47, 51.
• § 4.3: #3-8 all, 9, 11, 13, 35, 45.
• § 5.3: #1-5 all, 11-19 odd, 23, 25, 27, 33.

Links of Interest for Math 95

• Here's a link to a nice Unit Circle Diagram showing the terminal rays for all the "elementary angles" together with the coordinates of the corresponding points on the unit circle. You should become very familiar with the material in this diagram.
• Dave's Short Trig Course is a very nice supplementary resource for your study of trigonometry. The diagram at the top of the opening page shows the natural relationships between the sine, cosine, tangent, and cotangent functions and basic triangles associated with the unit circle. Note also that nearly all the figures on the site are "dynamic", meaning you can "click and drag" on certain points and see the diagrams change into different configurations (while still maintaining the "relationships" under consideration). "Dave's Short Trig Course" differs from our course text in that it begins with a "triangle approach" (rather than the unit circle approach) ...so reading and studying his development of the basic concepts of trig can provide an alternate viewpoint to our book (and experimenting with the many interactive graphics can be enjoyable & enlightening).
• xFunctions is a Java applet that will run in most recent versions of Firefox, Safari, Internet Explorer, or other Java capable browsers. (Be patient, it may take a minute to load the Java code into your browser.) xFunctions has eight different "utility screens" that allow you to:
  • View the graphs of many interesting function, and use the mouse to trace over the curve while reading off x and f(x) values.
  • Graph up to eight function on the same screen (in different colors) to compare behaviors.
  • Animate families of functions.
  • ...and many other capabilities related to Calculus.

  More links for Math 95 can be found within the "Math Links Page". Here is a shortcut to the trigonometry links on that page.

Mathematica Player and Interactive Notebooks

1. To begin, go to the Mathematica Player download web page, and follow the steps given there for downloading and installing the program onto your computer. Be aware that this is a fairly large file download...so it may take a few minutes with a DSL internet connection (or longer with slower internet connections).
2. Once the downloaded is finished you should be prompted by pop-up menus on how to install the program. This should be fairly relatively straightforward (at least it was on my Mac.). If you have difficulties with this please talk to me after class, or come by my office hours for help. (Alternatively, you might ask a "computer savvy" friend for some help with this part.)
3. After you've installed Mathematica Player you can download any interactive Mathematica notebook file (or ".nbp file") and save the file to your hard disk. You can then open the file with Mathematica Player, where you'll be able to read the notebook and access its interactive features.

Course Notebook Files

• The link for the first Mathematica Player notebook for our course is here: 3_TrianglesIn1stQuad.nbp. When you click the preceding link, it should either copy the file to your computer's default download location or open as a (strange looking) text file in your browser window. (In the latter case, save the file via your browsers "File" menu.) Next, start up the Mathematica Player program, choose "Open File" from the "File Menu" of Mathematica Player, and select your downloaded copy of the file "3_TrianglesIn1stQuad.nbp" from the location where it was saved on your computer. (Or, depending on how your computer is set up, you may be able to just double-click the icon for the file to open it in Mathematica Player.)

  This notebook provides three closely related interactive diagrams which illustrate the relationships of the six trig functions with side lengths of three associated triangles in the first quadrant. You can choose an acute angle (in degrees) by dragging a slider and the side lengths in the triangles will dynamically adjust as you move the slider. The values of the six trig functions of your selected angle will also be displayed (and updated as you move the slider).

  You'll be able to refer to the interactive diagrams in this notebook throughout the course to help motivate and support many of the central concepts we'll be developing (i.e. the domains and ranges of the six trig functions, their rectangular coordinate graphs, their inverse trig functions, cofunction and complementary angle relationships, etc.).

Other Useful Software for Math 95

• WinPlot is an extremely versatile, easy to learn and use program. It is completely free. However, it only runs under the Windows operating system. To get started using it, you can view a tutorial here.

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