Summer Self-Learning Trigonometry Course

(students will need a strong foundation in trig before taking honors precalculus, AP physics or IB physics)

If you want to learn trigonometry to prepare for your next class, this page will be your guide. Each section begins with website lessons (and, sometimes, notes), contains some optional and video resources, and ends with a review assignment so that you can judge whether you understand the concepts sufficiently. Each web and video lesson should open in its own window, and can be closed when finished to return you to this page. All review assignments, notes and lesson pages are PDF files that can be opened and printed from any computer using Acrobat Reader software (available for free from adobe.com website) or a PDF file reader. Depending on your browser, you may be given the option to open or save the document, in which case you should choose "open" (if you need to print it, you can do so after it opens). If you are not given this option, choose the "preview" icon for a document that you only wish to view, and it will open inside this page. If you need to print the document, click on the link and you will be able to download it, then print it.

There is no credit offered for this work; it is simply to allow you to move ahead into a new class with the necessary information to be successful. If you have any questions about this course, or have problems with this page, please feel free to contact me at: ashucker@hbuhsd.edu. During the summer, I may not check my mail every day, but I will get back to you as quickly as possible. While I am happy to be a resource regarding webpage or usage issues, I am not volunteering to tutor anyone through this course. The class for which you are preparing will require a great deal of self-directed learning, and this course will give you a chance to practice that skill. I sincerely hope that this course proves accessible and valuable to you, and that the information you acquire here assists you next Fall. ---Mr. Shucker

Unit 1--Angles in Trigonometry

In geometry, angles are always measured in degrees as positive values between 0 and 180. In trigonometry, angles are measured in two different units and in any direction and any size. This section will introduce you to a different way of measuring angles that will be necessary for the rest of the course.

Lesson 1-1: Angles and Their Measurement

(Optional) Video-Standard Position and Coterminal Angles

Lesson 1-2: Radian Measure (skip Problems 3-5)
(Optional) Video-Converting Between Degrees and Radians

(Optional) Angle Review

Unit 1 Review Assignment

Unit 2--Trigonometric Functions

While you have probably learned about sine, cosine and tangent in geometry (briefly), it is important to know that the "definitions" that you learned for these (yes, I am talking about SOH-CAH-TOA) are not definitions at all, but one very limited application of these functions (and there are three others just for fun). Here you will learn the true definitions of all six functions and how they work with the angles described in the previous section. Then you will review the solving of right triangles that was always fuzzy in geometry (unless you were one of the lucky ones).

Lesson 2-1: Functions on the Graph
(Optional) Video-Trig Functions from a Point

Lesson 2-2: Common Values of Trig Functions

Lesson 2-3: Signs in Different Quadrants

(Optional) Video-Using Special Right Triangles for Trig

Print and Complete this Table Using What You Have Learned

Lesson 2-4: Solving Right Triangles

(Optional) Video-Solving Right Triangles Part 1

(Optional) Video-Solving Right Triangles Part 2

Unit 2 Review Assignment

Unit 3--Solving Other Triangles

We have discussed how to solve right triangles using trigonometry (and a calculator, of course). With a few new formulas, it is possible to solve any kind of triangle if you are given the right information. This section will show you how. The first link will bring up a note page with all the information you will need to solve these triangles, including instructions about what to do in what order. Printing this page out is generally a good idea. The problem types are named by the position of the given information, using the notations from congruent triangles in geometry (everybody's favorite). So, if you are given the lengths of two sides and the size of the angle that connects them, we would call that a "side-angle-side" problem, which we abbreviate SAS. Each tutorial covers one type of problem solving for just one part. These will show you clearly how to apply each formula and what common mistakes to watch out for.

Notes (to print and keep)

Lesson 3-1: Solving All Triangles: Law of Sines

Lesson 3-2: Solving All Triangles: Law of Cosines

Lesson 3-3: Solving All Triangles: Ambiguous Case

Unit 3 Review Assignment

Unit 4--Trigonometric Identities

Formulas that are true regardless of the values of the variables are called "identities," but it's just a fancy word for formulas. In higher level math, problems will often have trig functions in them, and will look terrible. If you know how to use your trig identities, you can take a messy problem and rewrite it in a much simpler way. This makes the problem easier, and so this is a very important skill. The first link will again bring up a note page. It includes all the identities in all their forms. Most students do not try to memorize all the forms since they can be readily found from the originals using simple algebra. They are included simply to show the number of ways that these identities could look. In this section, you will use only two methods: substitution (replacing something with what the identity says it is equal to) and simplification (it's just algebra...it only looks different because of the "sin x" and "tan y"). The tutorial includes examples which should be worked out before moving on.

Notes (to print and keep)

Lesson 4-1: Introduction to Trig Identities (click on the Answer link for each example. LHS stands for Left-Hand Side [of the equation]. RHS is the right side)

Lesson 4-2: More with Trigonometric Identities (study this page through Example 6, then stop)

(Required) Video-Simplifying Trigonometric Expressions Using Identities Part 1
(Required) Video-Simplifying Trigonometric Expressions Using Identities Part 2
(Required) Video-Simplifying Trigonometric Expressions Using Identities Part 3
(Required) Video-Simplifying Trigonometric Expressions Using Identities Part 4
(Required) Video-Simplifying Trigonometric Expressions Using Identities Part 5
(Required) Video-Simplifying Trigonometric Expressions Using Identities Part 6

Unit 4 Review Assignment