Study Guide Precalculus

About the Author Janet Lee Adams received a Bachelor of Arts in Mathematics (secondary education) from Asbury College in Wilmore, Kentucky; a Master of Science in Operations Research from the University of Kentucky in Lexington, Kentucky; and a Master of Arts in Teaching Mathematics, also from the University of Kentucky. She taught a variety of mathematics courses in high school for 15 years and currently teaches classes at the Pennsylvania State University, Worthington Scranton Campus. She has served as a speaker at a number of mathematics conferences at the regional, state, and national levels. Janet is a member of the Pennsylvania Council of Teachers of Mathematics and of the Northeastern Council of Teachers of Mathematics. About the Reviewer Nathan C. Carter received a Bachelor of Arts in both Mathematics and Computer Science from the University of Scranton in Scranton, Pennsylvania. He completed his postgraduate work at Indiana University in Bloomington, Indiana, where he earned a Master of Science in Computer Science and a doctorate in Mathematics. Dr. Carter is currently teaching mathematics courses at Bentley University, Waltham, Massachusetts. His research includes articles on mathematical logic and social network analysis, and educational software development projects in group theory visualization and teaching mathematical proofs. Copyright © 2009 by Penn Foster, Inc. All rights reserved. No part of the material protected by this copyright may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording, or by any information storage and retrieval system, without permission in writing from the copyright owner. Requests for permission to make copies of any part of the work should be mailed to Copyright Permissions, Penn Foster, 925 Oak Street, Scranton, Pennsylvania 18515. Printed in the United States of America All terms mentioned in this text that are known to be trademarks or service marks have been appropriately capitalized. Use of a term in this text should not be regarded as affecting the validity of any trademark or service mark. INSTRUCTIONS TO STUDENTS 1 LESSON ASSIGNMENTS 7 LESSON 1: EXPONENTS, LOGARITHMS, SEQUENCES, AND SERIES 9 EXAMINATION—LESSON 1 41 LESSON 2: TRIGONOMETRIC FUNCTIONS 47 EXAMINATION—LESSON 2 75 LESSON 3: ANALYTIC TRIGONOMETRY 81 EXAMINATION—LESSON 3 95 LESSON 4: ADDITIONAL TOPICS IN TRIGONOMETRY 101 EXAMINATION—LESSON 4 123 LESSON 5: SYSTEMS OF EQUATIONS AND INEQUALITIES 129 EXAMINATION—LESSON 5 147 iii Contents Contents YOUR COURSE Mathematicians generally consider a course in precalculus to be an in-depth transition from the studies of algebra and trigonometry to the study of calculus. Algebraic topics in precalculus concentrate more on modeling real-world data than do those in intermediate algebra. In precalculus, trigonometry (triangle measurement) is taken outside triangles and is defined on a unit circle. In addition, you’ll be introduced to advanced topics not covered in algebra or trigonometry. The result is a course that will allow you to go beyond elementary word problems to advanced applications of your knowledge. You’ll apply the skills you learn to the areas of business, manufacturing, scientific research, physics, and cycles in nature and the human body—to name a few. In addition, you’ll need the skills you learn in this course to study calculus, which is without a doubt one of the most important area of mathematics ever developed. Whether or not you plan to continue in your study of mathematics, however, doesn’t mean that this course has no value in and of itself. Any academic study in which you engage will make you a better thinker and problem-solver for life. OBJECTIVES When you complete this course, you’ll be able to ■ Solve equations, including exponential, logarithmic, and trigonometric ■ Graph exponential, logarithmic, and trigonometric equations and equations in polar form ■ Solve systems of equations using substitution and addition methods ■ Graph solutions to inequalities in the coordinate plane ■ Graph solutions to systems of inequalities in the coordinate plane ■ Compute sums of finite and infinite series 1 Instructions Instructions ■ Express a series in summation notation ■ Convert angles measured in radians to degrees and vice versa ■ Solve triangles using right triangle trigonometry, the Law of Sines, and the Law of Cosines ■ Verify trigonometric identities ■ Plot points in the polar coordinate system ■ Convert points and eq