Customer Reviews

Trigonometry

5 star:		(5)
4 star:		(2)
3 star:		(0)
2 star:		(1)
1 star:		(1)

 

 

This text, which is designed as a supplement to a trigonometry course, is noteworthy for the clarity of its explanations, the connections it draws between trigonometry and other mathematical topics, its many challenging problems, and its numerous worked and illustrated examples. Of particular interest are the appendices to the later chapters in which the authors relate trigonometry to Pythagorean triples, use sequences of trigonometric functions to approximate pi, and introduce Fourier series.

After reviewing the geometry of the triangle, the authors cover right triangle trigonometry, the relationship between trigonometry and the geometry of the triangle, unit circle trigonometry, trigonometric formulas and identities, graphs of trigonometric functions, and inverse trigonometric functions. The authors make every effort to explain why the results hold and how to use them. Rather than presenting a self-contained treatment, the authors make every effort to connect trigonometry with other branches of mathematics, thereby providing the reader with many fascinating insights.

The problems are designed to be challenging. The reader who diligently studies the numerous worked examples in the text and works through the problems will acquire considerable knowledge of the subject. Solutions to the problems are not provided in the text.

I also highly recommend the other texts in the Gelfand School Outreach Program. They include The Method of Coordinates, Algebra, and Functions and Graphs (Dover Books on Mathematics).

Finally - a trig book that doesn't talk down to students. Gelfand treats his readers as intellegent, curious, and competent. This goes far ... especially with kids.

Most other trig books are written by educational consultants who view the subject as a odorous swamp that you have to slog through. They distract the reader with glitzy graphics and useless photos. No such chartjunk here. It's from someone who loves the subject, and places the mathematics first.

I feel like an avuncular mathematician is showing me the delights of trig ... indeed, he seems to revel in sines, cosines, and tangents. Several of the problems have tickled my 10 year old son: "Dad! Did you know that the area under the first half of the sine curve is exactly 2?"

Aaah. Now *that's* a great trig book!

I rarely compose reviews even if I happen to really appreciate a book. But THIS is one of those rare exceptions!Gelfand (who also happens to rank among the 20th Century's most renowned and prolific Mathematicians ... I noticed that no reviewer has mentioned this little fact) has written an exceptionally clear and concise, easy to read and to digest text concerning Trigonometry with advancement to higher education in mind. The perfectly logical format and development is novel, very inspiring, coaxing the reader to read on and on and one truly begins to learn right from the first sentence. The reader requires little in the way of prior knowledge and yet, I am convinced, will come away with an enthusiasm for this subject (and hopefully for Mathematics in general).
I am a member of a Mathematical Honor Society and of the Mathematical Association of America but I must confess that I was a poor math student, had some very poor teachers and, thanks to some inspiring individuals along the way, managed to discover the real magic and beauty of Math before it was too late (although I have spent the better portion of my professional life compensating for the failures of my former teachers!).
This text represents the way Math should be taught in schools. I believe that any frustrated math student will benefit from this text (and probably the other texts also by Gelfand).

This book is a very nice change away from the overly analytical approach that most trigonometry texts take nowadays. In my view something is lost when the geometric aspects are not emphasized. There is some fantastic geometry in this book, and I especially liked the connection between the sine addition formula and Ptolemy's theorem for quadrilaterals inscribed in a circle. Those kinds of connections are not only neat in themselves, but I think they help to understand the material better. I think they can spark students' interest more than the dull plug-in-the-numbers types of exercises in most books.

Speaking of the exercises, many of them are excellent. As some other reviewers have mentioned, it's nice to see a book at this level not insult the intelligence of its readers. I wish more elementary math textbooks were like this.

The only criticism I have is that there are lots of errors and typos in the book, enough to make me give it only 4 stars instead of 5. For instance, in Exercise 8 on p.147 it asks the reader to prove that (cos a)^2 <= cos(2a). Of course, that inequality should be reversed. And there are many more annoying little errors like that, which makes me believe that no one actually proofread the book.

I enjoyed this textbook, especially the way some subjects were so well explained. Not only does this text cover a good bit of material, but it also reveals the way in which the author thinks about this subject. I have noticed, both with this text and the previous two which I have commented on, that certain aspects of the subject become much more transparent or understandable when reexamined with a keener mathematical ability than, at least I possessed, when I was first exposed to these subjects in high school. I had no special interest in math at that time. The limited reexposure one has to trigonomety and geometry as one learns new areas of mathematics in college doesn't seem to do justice to these foundation areas of math.

I had purchased this book based on all of the positive reviews from this website and others. However, I was not at all happy with the result. The book itself does not explain anything. It makes learning a chore and kills every ounce of motivation to learn math. My two recently purchased Calculus books (Calculus Made Easy and A First Course in Calculus) made the subject fun and motivating. Everything was explained thoroughly and the solutions were given unlike this Trigonometry book.

Simply put - no solutions, no explanations, and no motivation to learn. It is not a good book for anyone wishing to self learn Trigonometry.

Good luck with your purchases!

Books
This is a very good Trig book. However, there was no offer of an answer book. I will teach a course using this book. Can you give me a site where I can get an answer book? With the answer book I could give 5 stars.

I usually buy books that have good feedback because it has served me well in the past, but unfortunately this isn't the case with this book. The author couldn't have picked a more perplexing way to explain this subject. Yes it's filled with problems, but what good are the problems if you don't have the correct answer nor do you have an explanation on how to solve them. Don't let the wonderful reviews fool you. If you still think it's worth a try, then I advise for you to look at a copy before buying.

So I bought this book for some Trig class I signed up for at the last minute. I didn't know what to expect. I skimmed through the book and saw triangles everywhere. I figured that a few triangles should not be so difficult to figure out- the measurements and all. It's a skimpy little book, but there sure is a lot of info crammed in there. I studied hard. I had dreams of triangles floating around, suspended in the air. I could not get triangles off my brain. Day and night- triangles and more triangles. I think I just got sick of looking at triangles come final exam, because I went out and got hammered to get them off my mind just hours before the exam. I'm not BSing you either. To make a long story short, I took the exam while under the influence of alcohol. It worked, the booze got the triangles off my brain, but the timing was not good because I had to think about triangles in order to finish the darn exam. I had a perfect GPA until that Trig exam. I did manage to pull off an A- on the exam, which surprised the heck outta me. Now I try to not let triangles get the best of me anymore. I'm angry at them, but at the same time I understand them. Triangles deserve respect. Don't be boozin' before an exam. This was a good book and I recommend it highly. But some advice first; don't be square and let the triangles shape your mind- think outside the box and you'll do fine, circle the correct answers if you can, and come at problems from different angles.