# KIM MALTMAN'S MINI-COURSE ON TRIG BASICS

## CHAPTER 2, SECTION C: THE BASIC GEOMETRICAL MEANINGS OF THE SIX TRIG FUNCTIONS

OVERVIEW:

This section of Chapter 2 provides explicit geometrical definitions of the six trig functions sine, cosine, secant, cosecant, tangent and cotangent in terms of the ratios of the sides of right-angle triangles. These definitions represent the most basic meaning of these functions. The topics to be covered are:

• why the ratios of sides of a right-angle triangle (and hence all of trig functions, which are defined by these ratios) depend only on the shape of the triangle, and not its overall size;

• why the shape of a right-angle triangle is completely specified by giving one of its two non-right angles (and hence why the trig functions are determined by giving just the one angle needed to specify the shape of the right-angle triangle in question);

• the geometrical ideas of the "hypoteneuse", and the sides "opposite" and "adjacent" to a given angle in a right-angle triangle, and the definitions of the six trig functions in terms of these concepts.

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 this background information, you can proceed directly to the contents of the current section of the course by clicking HERE.

BACKGROUND MATERIAL (AND LINKS):

For this section of the course you should be familiar with

• the geometrical meaning of angles and angular measure, as well as the basic conventions used in assigning an angle to a given direction in the plane (reviewable by reading (or re-reading) Section (b) of Chapter 1 of the course); and

• the basic fact that the sum of the three interior angles of any triangle is π radians (180 degrees) (reviewable by reading (or re-reading) Section (a), of Chapter 2 of the course).

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