, Theory and Problems of
TRIG 0 N0 METRY
Third Edition
WITH CALCULATOR-BASED SOLUTIONS
FRANK AYRES, JR., Ph.D.
Former Professor and Head, Department of Mathematics
Dickinson College
ROBERT E. MOYER, Ph.D.
Professor of Mathematics
Fort Valley State University
SCHAUM’S OUTLINE SERIES
McGRAW-HILL
New York San Francisco Washington, D.C. Auckland Bogoti
Caracas Lisbon London Madrid Mexico City Milan
Montreal New Delhi San Juan Singapore
Sydney Tokyo Toronto
,FRANK AYRES, JR., Ph.D., was formerly professor and head of the Department
of Mathematics at Dickinson College, Carlisle, Pennsylvania. He is the author
of eight Schaum’s Outlines, including CALCULUS, DIFFERENTIAL EQUA-
TIONS, 1st YEAR COLLEGE MATH, and MATRICES.
ROBERT E. MOYER has been teaching mathematics at Fort Valley State
University in Fort Valley, Georgia since 1985.He served as head of the Department
of Mathematics and Physics from 1992 to 1994. Before joining the FVSU faculty,
he served as the mathematics consultant for a five-county public school coopera-
tive. His experiences include twelve years of high school mathematics teaching
in Illinois. He received his Doctor of Philosophy in Mathematics Education from
the University of Illinois in 1974. From Southern Illinois University he received
his Master of Science in 1967 and his Bachelor of Science in 1964, both in
Mathematics Education.
Schaum’s Outline of Theory and Problems of
TRIGONOMETRY
Copyright 0 1999, 1990, 1954 by The McGraw-Hill Companies, Inc. All rights reserved. Printed
in the United States of America. Except as permitted under the Copyright Act of 1976, no part of
this publication may be reproduced or distributed in any form or by any means, or stored in a data
base or retrieval system, without the prior written permission of the publisher.
3 4 5 6 7 8 9 10 PRS PRS 9 9
ISBN 0-07-006893-3
Sponsoring Editor: Mary Loebig Giles
Production Supervisor: Pamela A. Pelton
Editing Supervisor: Frank Kotowski, Jr.
Library of Congress Cataloging-in-PublicationData
Ayres, Frank, 1901-
Schaum’s outline of theory and problems of trigonometry : with
calculator-based solutions / Frank Ayres, Jr., Robert E. Moyer. -
3rd ed.
p. cm. - (Schaum’s outline series)
Includes index.
ISBN 0-07-006893-3
1. Trigonometry-Outlines, syllabi, etc. 2. Trigonometry-
Problems, exercises, etc. I. Moyer, Robert E. 11. Title.
QA53 1 .A97 1998
5 16.24-4~21 98-40457
CIP
, In revising the second edition, the strengths of the prior editions were retained while reflecting the changes
in the study of trigonometry during the last ten years. This edition deletes the use of logarithms entirely,
increases the use of calculators, and changes from the column form of working identity problems to the
horizontal continuous equation form. Tables are still provided for finding trigonometric function values in 10-
minute intervals, tenth of a degree intervals, and hundredth of a radian intervals. The review of geometry is
still provided in an appendix.
The book is complete in itself and can be used equally well by those who are studying trigonometry for
the first time and those who are reviewing the fundamental principles and procedures of trigonometry.
Each chapter contains a summary of the necessary definitions and theorems followed by a solved set of
problems. These solved problems include the proofs of the theorems and the derivation of formulas. The
chapters end with a set of supplementary problems with their answers.
Triangle solution problems, trigonometric identities, and trigonometric equations require a knowledge of
elementary algebra. The problems have been carefully selected and their solutions have been spelled out in
detail and arranged to illustrate clearly the algebraic processes involved as well as the use of the basic
trigonometric relations.
ROBERTE. MOVER
TRIG 0 N0 METRY
Third Edition
WITH CALCULATOR-BASED SOLUTIONS
FRANK AYRES, JR., Ph.D.
Former Professor and Head, Department of Mathematics
Dickinson College
ROBERT E. MOYER, Ph.D.
Professor of Mathematics
Fort Valley State University
SCHAUM’S OUTLINE SERIES
McGRAW-HILL
New York San Francisco Washington, D.C. Auckland Bogoti
Caracas Lisbon London Madrid Mexico City Milan
Montreal New Delhi San Juan Singapore
Sydney Tokyo Toronto
,FRANK AYRES, JR., Ph.D., was formerly professor and head of the Department
of Mathematics at Dickinson College, Carlisle, Pennsylvania. He is the author
of eight Schaum’s Outlines, including CALCULUS, DIFFERENTIAL EQUA-
TIONS, 1st YEAR COLLEGE MATH, and MATRICES.
ROBERT E. MOYER has been teaching mathematics at Fort Valley State
University in Fort Valley, Georgia since 1985.He served as head of the Department
of Mathematics and Physics from 1992 to 1994. Before joining the FVSU faculty,
he served as the mathematics consultant for a five-county public school coopera-
tive. His experiences include twelve years of high school mathematics teaching
in Illinois. He received his Doctor of Philosophy in Mathematics Education from
the University of Illinois in 1974. From Southern Illinois University he received
his Master of Science in 1967 and his Bachelor of Science in 1964, both in
Mathematics Education.
Schaum’s Outline of Theory and Problems of
TRIGONOMETRY
Copyright 0 1999, 1990, 1954 by The McGraw-Hill Companies, Inc. All rights reserved. Printed
in the United States of America. Except as permitted under the Copyright Act of 1976, no part of
this publication may be reproduced or distributed in any form or by any means, or stored in a data
base or retrieval system, without the prior written permission of the publisher.
3 4 5 6 7 8 9 10 PRS PRS 9 9
ISBN 0-07-006893-3
Sponsoring Editor: Mary Loebig Giles
Production Supervisor: Pamela A. Pelton
Editing Supervisor: Frank Kotowski, Jr.
Library of Congress Cataloging-in-PublicationData
Ayres, Frank, 1901-
Schaum’s outline of theory and problems of trigonometry : with
calculator-based solutions / Frank Ayres, Jr., Robert E. Moyer. -
3rd ed.
p. cm. - (Schaum’s outline series)
Includes index.
ISBN 0-07-006893-3
1. Trigonometry-Outlines, syllabi, etc. 2. Trigonometry-
Problems, exercises, etc. I. Moyer, Robert E. 11. Title.
QA53 1 .A97 1998
5 16.24-4~21 98-40457
CIP
, In revising the second edition, the strengths of the prior editions were retained while reflecting the changes
in the study of trigonometry during the last ten years. This edition deletes the use of logarithms entirely,
increases the use of calculators, and changes from the column form of working identity problems to the
horizontal continuous equation form. Tables are still provided for finding trigonometric function values in 10-
minute intervals, tenth of a degree intervals, and hundredth of a radian intervals. The review of geometry is
still provided in an appendix.
The book is complete in itself and can be used equally well by those who are studying trigonometry for
the first time and those who are reviewing the fundamental principles and procedures of trigonometry.
Each chapter contains a summary of the necessary definitions and theorems followed by a solved set of
problems. These solved problems include the proofs of the theorems and the derivation of formulas. The
chapters end with a set of supplementary problems with their answers.
Triangle solution problems, trigonometric identities, and trigonometric equations require a knowledge of
elementary algebra. The problems have been carefully selected and their solutions have been spelled out in
detail and arranged to illustrate clearly the algebraic processes involved as well as the use of the basic
trigonometric relations.
ROBERTE. MOVER
