Trigonometry, An Individualized Approach - Textbook Directions to the Student

You are about to begin a new, successful experience in learning mathematics because this textbook can be of tremendous assistance to you. It was written to provide true instruction and it will teach you all you need to know if you use it as described below.

First, however, you must start a process of making sense out of mathematics. Students who ask “WHY” questions in mathematics become good at the subject because it really isn’t just a “bunch of meaningless rules.” Students who skip the “WHY” questions and try to learn “HOW” to do each type of problem find there are more types of problems than they can memorize successfully. The more you understand, the better you will remember and the less you will need to memorize. Every mathematic process has an answer to any “WHY” question you want to ask and this book tries to provide those answers, but if you don’t find them here then ask anyone who will listen. Just the process of asking “WHY” questions will, by itself, improve your ability to learn mathematics. Make a habit of asking “WHY” questions.

Now to the specific directions for this book. The most important part of this book is its frames. If you look at almost any page of the text, you will see a list of numbered items which are called frames. Each frame is separated into a left column and a right column. The left column of a frame gives you some information and a question (problem) to answer. Do the question and then look at the book’s answer which is printed in the right column of the frame. If your answer is the same as the book’s, then you have learned the lesson of the frame and you should continue to the next frame. If your answer is different from the book’s, then you have missed the lesson of the frame and need to get help before proceeding further. That help may be simply re-reading the frame, but if that is not sufficient then seek out a teacher, friend, or the e-mail system to get you back on the right track.

The frames are the most important part of the book because they are the only part of the text where you learn the mathematics. All other parts of the book are intended to give you information about how well you have learned the mathematics, but only in the frames do you learn mathematics. If you do the frames well, everything else will follow accordingly. If you skip the frames because you “kind of” understand them, then you will make learning unnecessarily difficult.

Each chapter ends with a Mastery Test and when you finish the chapter you will learn how well you have learned it by grading the test. If any problem seems difficult, you will find that you need to restudy its section. Answers for all of these problems are given at the back of the book.

Feedback Exercises are at the end of each unit of a chapter. The problems of a Feedback Exercise give you a method of evaluating your work each day. Answers for all of these problems are given at the back of the book. If you have any trouble with a Feedback Exercise, you will find help in the unit just completed.

Every problem in this book has an answer given for it. Your learning successfully depends upon knowing, as you go along, whether you are right or wrong. You must accept the responsibility for determining the accuracy of your work. Looking at the answer is one way for you to meet that responsibility. Learning how to check an answer is another way to meet the same responsibility. Regardless of your method, you are expected to always know whether your work has been done correctly.

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