What's the Difference Between Trigonometry and Geometry?

[Miike012]

This upcoming semester I will be taking trig... I wanted to know what the diff is between trig and geometry... are they both the same thing?

Anyways, I really want to increase my algebra skills and trig skills as much as possible before I go nto calc and physics... are there any good books on trig, geometry or algebra?

 

[Mark44]

Trigonometry (literally "triangle measure") is more specialized than geometry in that it deals with triangles rather than arbitrary geometric objects.

Trigonometry and algebra are often combined in precalculus courses. There are lots of books. Do you know what text you will be using for your class?

 

[Miike012]

I will be using this book...
http://www.abebooks.com/servlet/BookDetailsPL?bi=3371653448

But do you know of any books that are not school textbooks... I want something that goes a little deeper

 

[Mark44]

I hope you have that book in the link already, since it was sold out when I clicked the link. Off the top of my head I don't know of any books on trig that aren't school texts. You might do a search with "trigonometry" on amazon.com. I'm sure they would have plenty of titles available.

 

[Miike012]

Yeah I know, I will have to get one at the text store from school.. I know they have the book. But I will just have to search around.

 

[saim_]

Plane Trigonommetry by S.L. Loney. The famous book that kept Ramanujan interested through secondary school. This book probably contains more trig than any high schooler, even the motivated ones, would care to know. Also, its quite old and might contain somethings quite useless for a modern trig course. But still, if you want to go really deep into trig, this book is your friend. More than a hundred years after its first print, it is still one of the good sources to refer to if you want to work on really good, challenging problems like for olympiads.

 

[Miike012]

thank you so much.. i will search for it now

 

[Miike012]

is this it...
https://www.amazon.com/dp/1418185094/?tag=pfamazon01-20


and do you know of a good algebra book to?

thanks again.

 

[saim_]

Yes that is the one I was talking about. I do know an old classic for algebra as well but a word of caution: by supplementing these for textbooks you could set too difficult a task for yourself and you may become discouraged soon. Use them rather as reference books, maybe to read proofs your teacher skips.

Higher Algebra (by H.S. Hall and S.R. Knight)
https://www.amazon.com/dp/1402179650/?tag=pfamazon01-20

Its also almost just as old as Loney's book. It has an even dryer prose and I'd say its much tougher than Loney's Plane Trig. Some of the chapters in it are usually only taught at university level these days like number theory, linear algebra, continued fractions and some other stuff as well. However, most of the theory is at high school level algebra but in much more rigorous detail.

 

[Miike012]

Ha are they really that difficult...? I think I can handle them (I hope lol) currently I am reading a number theory book and calc book ( never taken them) and I am doing just fine... so hopefully these ones arnt any more difficult than the ones that I am reading currently.

 

[Miike012]

Ps. currently I am reading a book called "calculus an intuitive and physical approach." (Have you heard of it? if so what do you think about it?) anyways once I am done with the book I am looking for another more adcanced calc book, know of any? lol sorry I just keep asking you for books lol.

 

[Miike012]

Check out what I found... http://www.archive.org/details/higheralgebraseq00hall

on the left hand side click PDF...
is that the algebra book than you mentioned? If so I found it in a free pdf form.

 

[Herricane]

When i was in High school I used Trigonometry by I.M. Gelfand and M. Saul. There are some really awesome proofs that I didn't learn in my Trig class.

 

[Miike012]

This algebra book that I am looking at, if it is the one you are talking about, it is much diff than the one I have currently.

 

[saim_]

Yes this is the book I'm talking about.

Ha are they really that difficult...?

I think difficult would be the wrong word; they will have much much more details and proofs than will be required by a normal school level course. More than one can cover in a year or maybe even two. The extra theory won't be impossibly challenging but the problems can be very tough. For example, the end of book problems includes selection from tough university exams and even Math Tripos! The point of the warning is: don't be discouraged if sometimes its hard to understand something from the almost non-existent prose and the monotonous theorem-proof style of exposition; these books can be very dull. Modern texts are much better written but I'm not aware of any such book, aimed at high school students, with such in-depth study of things.


I haven't read the calculus book you mentioned however it seems like a good book. We just used our assigned text by Sowokowski and I tried Apostol on the side. For rigorous calculus, I'd suggest Apostol or Spivak but at least not until you have a grip on algebra and trig and have gone through all the basics of single variable calculus from an easier approach. Its not how much you can follow, but how much you can get out of a book. One can probably understand Apostol's first few chapters after 8th grade but he won't really benefit much from it as he doesn't have the general overview of the basics.

 

[middleCmusic]

Hey Mike,

If you didn't already find it, you can download that algebra book that was recommended as well on Google books here: http://books.google.com/ebooks?id=grQUWYejIq4C&num=10

Just click "Read on Your Device" at the right and scroll down to "Download as PDF"

 

[Miike012]

haha ok Saim, I am eating my own words lol... but it is really a cool book! this is what I have been looking for. thank you.

 

[Miike012]

thank you middlecmusic... its just my lucky day... getting to great books.