Getting Started
Do you wonder what the study of precalculus holds for you, and how this textbook can help you on your mathematical journey? The truth is that the folks who compiled this book for you enjoy mathematics, and we really just want you to like studying precalculus. As we tackle the various topics in this book, we hope that you embrace the natural challenge that comes with visualizing a unit circle, understanding what the different trigonometric functions and equations do, and plotting points on a polar grid (just to name a few of the interesting and thought-provoking things we’ll be doing together!). We hope that you enjoy contemplating novel ideas (can a circle actually be re-imagined as a function?!?) and that your inner math beast is revealed to you along the way! So join me in saying ¡Viva la Precalculus! What are we waiting for? Let’s start with some basic information about the formatting of this book.
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First, we’d like to provide some math notation for you. Virtually all notation is defined in the context of its first use in the book. The exceptions are listed in the following table:
| Mathematical Notation | Meaning |
| A={} | declares a set A |
| A={x:x satisfies some condition} | builds a set A out of elements subject to certain conditions |
| [latex]\mathbb{R}[/latex] | the set of all real numbers |
Next, the chapters of this book are organized into different sections. In the introduction to each chapter, you’ll find a table of Key Takeaways. Use this table to reference the important information included in the chapter.
Key Takeaways
- Bullet points will highlight the key takeaways from the chapter.
- These will outline the important topics you read to help you prepare for your coursework.
- These key points are the student learning objectives for the course.
At the beginning of each section in a chapter, you’ll see learning objectives listed in tables that look like this:
Learning Objectives
- Bullet points will highlight the important information for each section within the chapter.
At the end of each section, you’ll see links to outside media resources that might be useful to you, as well as additional problems that you can work through for extra practice. Answers to these additional problems can be found in a solution index at the end of the book.
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Finally, let’s set the stage for our journey together!
You take your cousin Mo downtown to sightsee in Hemisfair Park. Because Mo is from New Jersey, he’s dying to ride the elevator up the Tower of the Americas for an unobscured view of the horizon. You part with Mo, who heads towards the Tower while you grab an aquas frescas to cool off. As you take your last sip of this sweet nectar from the gods, Mo calls you from the top of the tower and wants you to join him. If the tower is 750 feet tall, and the angle of elevation from you to the top is 17o, how far of a walk do you have to meet your cousin? Do you go meet him? Explain why you do or don’t walk to the tower.
Before we can find an answer to this problem and others like it, let’s start with a review of functions, domain, and range in Chapter 1.
