Trigonometry 2001st Edition

by I.M. Gelfand (Author), Mark Saul (Author)

37 ratings

ISBN-13: 978-0817639143

ISBN-10: 0817639144

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In a sense, trigonometry sits at the center of high school mathematics. It originates in the study of geometry when we investigate the ratios of sides in similar right triangles, or when we look at the relationship between a chord of a circle and its arc. It leads to a much deeper study of periodic functions, and of the so-called transcendental functions, which cannot be described using finite algebraic processes. It also has many applications to physics, astronomy, and other branches of science. It is a very old subject. Many of the geometric results that we now state in trigonometric terms were given a purely geometric exposition by Euclid. Ptolemy, an early astronomer, began to go beyond Euclid, using the geometry of the time to construct what we now call tables of values of trigonometric functions. Trigonometry is an important introduction to calculus, where one stud ies what mathematicians call analytic properties of functions. One of the goals of this book is to prepare you for a course in calculus by directing your attention away from particular values of a function to a study of the function as an object in itself. This way of thinking is useful not just in calculus, but in many mathematical situations. So trigonometry is a part of pre-calculus, and is related to other pre-calculus topics, such as exponential and logarithmic functions, and complex numbers.

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Editorial Reviews

Review

"Cover[s] all of the basic topics that a high school or beginning university student should be expected to know.... There are...some nice touches; for example, a nice informal discussion showing that the sine of an angle in a right triangle does not depend on whether the sides are measured in inches or centimeters..."

―Choice

"Covers all the basics of the subject through beautiful illustrations and examples…. Throughout, the treatment stimulates the reader to think of mathematics as a unified subject."

― L'enseignement Mathématique

"As a teacher I enjoyed this book enormously and I will doubtless borrow many of the plums to spice up my lessons…. [For] that ideal student who is to be prepared to be challenged to think what the subject is really about, and has the patience to excavate the basic ideas for all they are worth before jumping on to the next chapter, it should prove to be a godsend."

―The Mathematical Gazette

"The authors tried to explain the results of trigonometry as simply as possible…. The exercises include a few problems of each routine type. Most of the problems exhibit a new aspect of the technique or object under discussion. One of the goals of this book is to prepare students for a course in calculus. We recommend it for teachers and students."

―Publicationes Mathematicae

Product details

Publisher : Birkhäuser; 2001st edition (June 8, 2001)
Language: : English
Paperback : 239 pages
ISBN-10 : 0817639144
ISBN-13 : 978-0817639143
Item Weight : 1.68 pounds
Dimensions : 5.98 x 0.55 x 9.02 inches

Best Sellers Rank: #234,003 in Books (See Top 100 in Books)
- #37 in Trigonometry (Books)
- #69 in Geometry (Books)
- #184 in Geometry & Topology (Books)

Customer Reviews:
37 ratings

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cole

Much Insight

Reviewed in the United States on December 15, 2016

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I.M. Gelfand is a wonderful mathematician and I have found his books very insightful. I used this book for self-study and was very pleased with it. The main shortcoming of the text is that there are no solutions to the problems. This is not a problem for most of the problems, but some are much more difficult than others. Also, a lot of the problems involve proof. This is typical of math text, but if you are not familiar with elementary proof it may be difficult to work through the problems. Lastly, as with any mathematics book the problems are essential to work through and not auxiliary!

3 people found this helpful

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Teresa Stephens

Far better than the run of the mill

Reviewed in the United States on June 12, 2014

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Trig is one of those subjects that gets short shrift, much like algebra. I have to say I think that's because it's taught to kids, who mostly have to take what's given to them. Gelfand eschews the "here, memorize this," approach. While developing the sines and cosines from the standard right triangles, he integrates them with algebra immediately so that you translate smoothly to dealing with them as functions with no clunky, baffling mechanical in-between stage. Most trig manuals are SO BORING even though they're loaded with applications and 4-color illustrations; this little black and white number is hardly bigger than a pamphlet, but it has everything you need and won't put you to sleep. Rightly called a classic.

6 people found this helpful

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Georgy

π-free trigonometry

Reviewed in the United States on January 12, 2020

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I just noticed that this book managed to go on for 5 chapters without ONCE mentioning π. I didn't even know this is possible for a trigonometry textbook. This is a perfect illustration of how they actually care about explaining concepts rather than defining empty technicalities!

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Amalfitano

Great

Reviewed in the United States on June 26, 2017

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Great book for reviewing and learning to think about the material with a bit more depth. Bought as an adult (who studied math in college no less), and it's a little easy but still stimulating and helped me review stuff that I never really gave enough attention to in high school. Probably a great book for kids.

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W. Wang

A great trigonometry introduction by a real mathematician

Reviewed in the United States on December 11, 2016

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A great trigonometry introduction by a real mathematician not some Ed.D's, Good for non-dummies!

4 people found this helpful

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LimehouseBlues

Terrific!

Reviewed in the United States on October 5, 2006

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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!

60 people found this helpful

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George C. Johnson

Innovative, clear, well written trigonomety textbook

Reviewed in the United States on April 6, 2007

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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.

14 people found this helpful

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L. D. Rafey

Outstanding Math Text

Reviewed in the United States on June 14, 2006

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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).

58 people found this helpful

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Dee

Kindle edition un-useable

Reviewed in the United Kingdom on December 18, 2020

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Kindle Edition - formatting of formulas is terrible, often overlaying text. Makes the book un-useable unfortunately.

C. Gilmartin.

Masterful.

Reviewed in the United Kingdom on March 30, 2012

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I am more and more impressed with Gelfand all the time. This book is fantastic! It is a must if you wish to build a real mathematical foundation and I have already begun recommending it to anyone who even remotely wishes to do so. It is written in a mature style and you are always given the impression that there is a grander truth beneath what is being stated, and as a result the reader is inclined to question and investigate the implications on his/her own. This combines to give the reader the feeling that they are actually doing some real mathematics; a stark contrast to the cold, uninformed sensation felt after working with a typical high school, question and answer, round peg in the round hole, "that's out of your reach so don't bother wondering", text book. If you want to learn/review trigonometry, from the ground up, then look no further this is your book.

4 people found this helpful

jeremy

Filled with an abundance of great information

Reviewed in Canada on February 26, 2014

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I purchased this soley based on my appreciation of the Algebra book belonging to the same series, which is PHENOMENAL.
The algebra book is a great stand alone all encompassing book, whereas the trigonometry book assumes a well grounded knowledge of many geometry concepts and doesn't always include the material required to solve the problems (which this book is comprised of almost entirely). With a secondary book in hand alot can be gained from this, the problems are thought provoking and insightful. However as stated previously, Trigonometry pales significantly in comparison to the Algebra book that I found to be immensely helpful as a stand alone book containing proofs for things as remedial as adding negative numbers.

One person found this helpful

Alan Hammond

trigonometry

Reviewed in the United Kingdom on November 3, 2013

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If you're looking up this book you are in a very niche and lonely edge of society do not despair other geeks are available, the book is also quite good if you're playing catch-up or doing a little remedial work.

One person found this helpful

矢野茂

英語の三角関数本

Reviewed in Japan on May 30, 2020

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こんな本が手に入るとは。

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