Unit 3

Chapter 5 – Analytic Trigonometry

Unit 3 in the course, chapter 5 in the textbook, continues building on the previous trigonometry content.

Hopefully you remember the pre-algebra "properties," such as the Distributive Property which states that A(B+C) = AB + AC for all real numbers A, B, & C.

Similarly, we start this unit by learning the trigonometric "identities," such as one of the Pythagorean Identities which states that cos²A + sin²A = 1 for all real numbers A.

One of the biggest mistakes that students make is believing that this material is all about memorizing formulas. You'll hear me claim plenty of times that you should not be simply memorizing any of this material!

To be successful in this unit, your challenge is develop a clear picture (either on paper or in your head) that allows you to clearly see why each and every one of these identities makes perfect sense.

My strong beliefs about this unit:

- Seeing the beautiful and elegant underlying logic behind the identities makes the subject much more interesting
- We will learn several dozen identities in all, and very few students could effectively memorize all of them
- If you clearly understand why these identities work, you'll also see that they are all interrelated, and the relations between them will help you see this as a single united subject rather than a bunch of random facts
- Not only is memorization a boring way to approach mathematics, but if you simply memorize several dozen formulas that make no sense to you, you'll have completely forgotten them when you need them in Calculus

I believe this is the most fascinating unit in all of PreCalculus and every year there are a good number of students who also find it very interesting. However, this is also the unit that causes the most misery for students who don't get off on the right foot. Please resolve to stay caught up and refuse to resort to rote memorization!

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