# KIM MALTMAN'S MINI-COURSE ON TRIG BASICS

## CHAPTER 3, SECTION D: AN EXAMPLE OF THE UTILITY OF THE UNIT CIRCLE PICTURE: TRIG FUNCTION VALUES FOR THE +x, -x, +y, OR -y AXIS DIRECTIONS

OVERVIEW:

This section of Chapter 3 gives a nice example of how useful the unit circle picture for the sine and cosine can be by showing how it is used to work out the trig functions of angles which correspond to directions along the +x, -x, +y and -y axes. These directions often present a problem to students because there is no obvious right-angle triangle to which such directions correspond. We will see that the unit circle picture makes it incredibly easy to figure out the values of the sine and cosine for each of these four directions and, from these, the values of those two of the remaining four trig functions (secant, cosecant, tangent and cotangent) which are defined for the direction in question. It will also make it obvious why two of these four additional functions must be undefined for each such direction.

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)

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

• the idea of using the unit circle picture for the sine and cosine, together with the algebraic relations expressing the tangent, cotangent, secant and cosecant functions as ratios involving the sine and cosine functions, to generalize the trig functions to all possible directions (reviewable by reading (or re-reading) Section (c) of Chapter 3 of this course)