## Contents

Preface

1 Trigonometric functions

Some definitions ; Set-square angles ; Consequences of Pythagoras’

theorem ; Exercise I

2 Trigonometric identities 13

Compound-angle identities ; The double-angle identities ; The half-angle

identities; The factor formulae ; Exercise 2

3 Trigonometric equations and their solution 20

The expression a cos () + b sin 0 ; The equation a cos () + b sin () = c;

Exercise 3

4 Other topics 28

Approximations for small angles; Inverse trigonometric functions ; The

sine and cosine rules ; The area of a triangle ; Exercise 4

Answers 36

Index 37

## Preface

Advanced level mathematics syllabuses are once again undergoing changes in

content and approach following the revolution in the early 1960s which led to

the unfortunate dichotomy between ‘modern ‘ and ‘ traditional’ mathematics.

The current trend in syllabuses for Advanced level mathematics now being

developed and published by many GCE Boards is towards an integrated

approach, taking the best of the topics and approaches of modern and traditional

mathematics, in an attempt to create a realistic examination target

through syllabuses which are maximal for examining and minimal for teaching .

In addition, resulting from a number of initiatives, core syllabuses are being

developed for Advanced level mathematics consisting of techniques of pure

mathematics as taught in schools and colleges at this level.

The concept of a core can be used in several ways, one of which is mentioned

above, namely the idea of a core syllabus to which options such as theoretical

mechanics, further pure mathematics and statistics can be added . The books

in this series are core books involving a different use of the core idea. They

are books on a range of topics, each of which is central to the study of Advanced

level mathematics, which together cover the main areas of any single-subject

mathematics syllabus at Advanced level.

Particularly at times when economic conditions make the problems of

acquiring comprehensive textbooks giving complete syllabus coverage acute,

schools and colleges and individual students can collect as many of the core

books as they need to supplement books they already have, so that the most

recent syllabuses of, for example, the London, Cambridge, AEB and JMB GCE

Boards can be covered at minimum expense. Alternatively, of course , the

whole set of core books gives complete syllabus coverage of single-subject

Advanced level mathematics syllabuses.

The aim of each book is to develop a major topic of the single-subject syllabuses

giving essential book work, worked examples and numerous exercises

arising from the authors’ vast experience of examining at this level. Thus,

as well as using the core books in either of the above ways, they are ideal for

supplementing comprehensive textbooks by providing more examples and

exercises, so necessary for the preparation and revision for examinations.

In this particular book we cover the requirements of non-specialist mathematicians

in basic trigonometry in accordance with the core syllabus of pure

mathematics now being included by GCE Examining Boards . It also meets the

requirements of the polytechnics and universities for entrants to degree courses

in mathematics-related subjects . No previous knowledge of trigonometry is

assumed; that is, the basic definitions are stated and the standard results are

derived , some by means of worked examples. While inevitably lacking experience,

the student should try to acquire and appreciate good technique, so that

more difficult problems may be tackled with confidence. Only the most elementary

knowledge of coordinates and the theorem of Pythagoras have been

assumed.

Confidence in using calculators which contain the trigonometric functions

and their inverses is essential both at ‘A’ level and beyond. No reference is

made to trigonometric tables in this book . The calculator is here to stay and

we must use it accurately where appropriate. Plenty of GCE-type examples

are provided throughout the book, both as exercises and as part of the text.