# KIM MALTMAN'S MINI-COURSE ON TRIG BASICS

## CHAPTER 5, SECTION B: IDENTITIES BASED ON PYTHAGORAS' THEOREM

OVERVIEW:

This section of Chapter 5 discusses three identities which follow from

• Pythagoras' Theorem

• the basic geometrical (right-triangle-based) definitions of the sine and cosine and

• the algebraic relations expressing the tangent, cotangent, secant and cosecant as ratios involving the sine and cosine.

The specific topics to be covered are:

• The basic trig identity sin2(θ) +cos2(θ)=1 and its relation to Pythagoras' theorem

• The related identities sec2(θ) =tan2(θ)+1 and csc2(θ) =1+cot2(θ)

• Uses of these identities (beyond just using them to replace two terms in an equation with one term)

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 quickly review it, click on the relevant link.

If you are already familiar with this background, 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 with

• the basic geometrical definitions of the sine and cosine 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 giving the tangent, cotangent, secant and cosecant 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)

Other more basic background topics which it may be helpful to review if you are coming to any of the background material sections listed above for the first time are

• the basic idea of angles and angular measure (reviewable by reading (or re-reading) the topics accessible via links on the main page of Chapter 1 of the course)