# KIM MALTMAN'S MINI-COURSE ON TRIG BASICS

## CHAPTER 3, SECTION C: GENERALIZING THE TRIG FUNCTIONS TO NON-FIRST-QUADRANT DIRECTIONS

OVERVIEW:

This section of Chapter 3 discusses how to go about naturally generalizing the definitions of the six trig functions from first quadrant angles (angles which naturally occur as non-right interior angles of right angle triangles) to all other angle values. The key perspective which makes this generalization natural is the unit circle picture for visualizing the sine and cosine. The unit circle picture, together with its relation to the underlying geometrical definitions of the sine and cosine functions, was introduced and discussed in detail in Section B of this chapter.

A list of the background material needed to follow the contents of this section is given below. If you are unfamiliar with one of the background topics, or feel you would like to review it, click on the relevant link.

If you are already familar with all of the background material, you can proceed directly to the contents of the current section of the course by clicking HERE.

For this section of the course, you should be familiar with

• the idea and geometrical meaning of angles and angular measure (reviewable by reading (or re-reading) the various sections of Chapter 1 of the course, which can be accessed by clicking HERE),

• the basic geometrical definitions of all six trig functions as the ratios of sides of the appropriate right angle triangles, phrased in terms of the concepts "hypoteneuse", "adjacent" and "opposite" (reviewable by reading (or re-reading) Section (c) of Chapter 2 of the course)

• the algebraic relations amongst the various trig functions of the same angle, especially those which allow the tangent, cotangent, secant and cosecant to be written in terms of the sine and cosine (reviewable by reading (or re-reading) Section (a) of Chapter 3 of this course) and

• the unit circle picture for the sine and cosine functions (reviewable by reading (or re-reading) Section (b) of Chapter 3 of this course)