Textbook in PDF format

Most math and science study guides are a reflection of the college professors who write them: dry, difficult, and pretentious. The Humongous Book of Trigonometry Problems is the exception. Author Mike Kelley has taken what appears to be a typical trigonometry workbook, chock full of solved problems—more than 750!—and made notes in the margins adding missing steps and simplifying concepts and solutions, so what would be baffling to students is made perfectly clear. No longer will befuddled students wonder where a particular answer came from or have to rely on trial and error to solve problems. And by learning how to interpret and solve problems as they are presented in a standard trigonometry course, students become fully prepared to solve those difficult, obscure problems that were never discussed in class but always seem to find their way onto exams.
The best way to develop trigonometry skills is by working out trigonometry problems. There’s no denying it. If you could figure this class out just by reading the textbook or taking good notes in class, everybody would pass with flying colors. Unfortunately, the harsh truth is that you have to buckle down and work problems out until your fingers are numb.
Most textbooks only tell you what the answers to their practice problems are but not how to do them! Sure your textbook may have 175 problems for every topic, but most textbooks only give you the answers. That means if you don’t get the answer right you’re totally out of luck! Knowing you’re wrong is no help at all if you don’t know why you’re wrong. Math textbooks sit on a huge throne, like the Great and Powerful Oz and say, “Nope, try again,” and you do. Over and over, usually getting the problem wrong. What a delightful way to learn! (Let’s not even get into why they only tell you the answers to the odd problems. Does that mean the book’s actual author didn’t even feel like working out the even ones?)
Even when math books try to show you the steps for a problem, they do a lousy job. Math people love to skip steps. You’ll be following along fine with an explanation and then all of a sudden bam, you’re lost. You’ll think to yourself, “How did they do that?” or “Where the heck did that 42 come from? It wasn’t there in the last step!” Why do math textbooks insist that in order to work out a problem on page 200, you’d better know pages 1 through 199 like the back of your hand? You don’t want to spend the rest of your life on homework! You just want to know when you’re supposed to use the law of sines and when you’re supposed to use the law of cosines, which you’ll learn in Chapter 13.
Just about every single kind of trigonometry problem you could possibly run into is in here. After all, this book is humongous! If 750 problems aren’t enough, then you’ve got some kind of crazy math hunger, my friend, and I’d seek professional help. This practice book was good at first, but to make it great, I went through and worked out all the problems and took notes in the margins when I thought something was confusing or needed a little more explanation. I also drew little skulls next to the hardest problems, so you’d know not to freak out if they were too challenging. After all, if you’re working on a problem and you’re totally stumped, isn’t it better to know that the problem is supposed to be hard? It’s reassuring, at least for me.
Introduction
Angles and Arcs
Right Triangle Trigonometry
The Unit Circle
Trigonometric Values of General Angles
Graphing Sine and Cosine Functions
Graphing Other Trigonometric Functions
Basic Trigonometric Identities
Advanced Trigonometric Identities
Inverse Trigonometric Functions
Simple Trigonometric Equations
Advanced Trigonometric Equations
Area of Triangles and Sectors
Oblique Triangle Laws
Vectors
Basic Vector Operations
Advanced Vector Operations
Parametric Equations and Polar Coordinates
Trigonometry of Complex Numbers
Appendicies
Table of Trigonometric Values
The Unit Circle
Formulas and Identities