- A brief introduction to the idea of identities (as distinct from more general equations) for students who have not yet had this idea made clear to them
- Identities between trig functions of the same angle which follow from Pythagoras' Theorem
- A brief summary of the remaining identities to be discussed in this chapter, toegether with an introductory discussion of how such identities are meant to be interpreted and used (including some specific examples for illustration purposes)
- Identities between trig functions of different angles associated with different, but naturally related, right-angle triangles
- The sine and cosine addition formulas (including the non-trivial geometric origin of these identities)
- Other identities which follow easily (with no need of memorization) from the sine and cosine addition formulas (e.g., the tangent and cotangent addition formulas, the double-angle and half-angle formulas, etc.)
- Pythagoras' Theorem (reviewable by reading (or re-reading) Section (b) of Chapter 2 of the course)
- the basic geometrical definitions of the sine and cosine functions as the ratios of sides of the appropriate right angle triangles (reviewable by reading (or re-reading) Section (c) of Chapter 2 of the course)
- the algebraic inter-relations amongst the six trig functions which allow the tangent, cotangent, secant and cosecant functions to be written as ratios involving the sine and cosine (reviewable by reading (or re-reading) Section (a) of Chapter 3 of the course)
- the unit circle picture for generalizing the sine and cosine functions, and from these, also the tangent, cotangent, secant and cosecant functions, from Quadrant I to Quadrant II, III and IV values of the relevant angle (reviewable by reading (or re-reading) Section (b) and Section (c) of Chapter 3 of the course)
- the alternate "flopped-over" triangle perspective for thinking about the relation between trig functions of first quadrant angles and the appropriately related second, third and four quadrant angles (reviewable by reading (or re-reading) Section (e) of Chapter 3 of the course)

This chapter of the course deals with identities amongst trig functions of either the same or different angles. Topics to be covered are:

**Links to files dealing with each of these new topics, as well
as links to earlier sections of the course which are particularly
relevant as background, are given in the "BACKGROUND MATERIAL LINKS"
and "LINKS FOR THE NEW CHAPTER 5 TOPICS" sections below.**

**BACKGROUND MATERIAL LINKS:**

The key background needed in order to follow the material in this Chapter of the course is a familiarity with

**LINKS FOR THE NEW CHAPTER 5 TOPICS:**

*Click on the link for the appropriate topic below for more information
on that topic. In general, it would be a good idea to go through the
material in the order listed, unless you are returning to this page
for a refresher on a particular topic (or topics) or are already
familiar with some of the topics from previous review.
*