A New Trigonometry

[dondigitalia]

Well worth the rather pricey $80.

lol, in my experience, that's cheap for a mathematical/scientific text. Some of my books cost over $200.

[Eternal]

Some of my books cost over $200.

Well - then you should look into getting Asian edition of the same books. You can usually get those at 1/5th of the original price - (I remember paying $100 for semester worth of books). They're brand new, and the only downside is a rather low quality of paper, and the fact that they are paperback instead of hardcover (which can be an advantage if you have to carry the damn thing all the time). You can usually get these books on Amazon, from individual sellers (assuming you don't have a friend in India who can ship them to you).

[dondigitalia]

A couple of friends of mine have recommended the same thing. My roommate, who is a Creative Writing major, had to take all sorts of Literature classes this semester, which collectively required him to buy 40-something books--yikes!!! By shopping on Amazon, he was able to cut the cost from over $500 to around $200. A $300 savings is definitely worth a little wait time in shipping!

[Franklin]

I've enjoyed the first chapter (pdf).

I am also going to buy the book. I have always had problems with trignometry. Nobody ever gave the definition of sine, cosine, and tagent to me, and I had to figure it out on my own. When I did, I found an absurd circular logic to them. cos (angle) = adjacent/hypotenuse. It was just a ratio that was universal - certainly it worked but I found the solution somewhat...brute-forcing your way to the solution. This seems to hold great potential.

Trig has really kept me away from the higher mathematics (which I am interested in greatly) because of all of the stuff I wrote above. Now I am going to purchase this book and see if its methods are any better.

Edit: It is so refreshing to read a the beginning of a math textbook and have the author explain "We are going to write things this way, because it will be useful to you when you go on to higher math to think of the concept in this manner."

What the hell. You cannot get rid of those things. That is like getting rid of gravity for Christ's sake. This is bullshit.

[y_feldblum]

Nothing is gotten rid of. The author uses superficially different methods to arrive at exact answers. One either uses a calculator or never computes angles in classical trigonometry; instead of computing angles, one algebraically manipulates expressions involving trigonometric functions using their identities - i.e., if one needs to find the cosine of an angle when the sine of that angle is known, one uses the identity (cos a)(cos a) + (sin a)(sin a) = 1, for all a, to find that the cosine in terms of the sine. Such methods of classical trigonometry appear to calculate angles, but they do not. In fact, they implicitly use the methods of rational trigonometry. Rational trigonometry is upfront about using these methods and is upfront about never calculating angles.

[dondigitalia]

Such methods of classical trigonometry appear to calculate angles, but they do not. In fact, they implicitly use the methods of rational trigonometry. Rational trigonometry is upfront about using these methods and is upfront about never calculating angles.

That is the best description of the relationship between classical and rational trig I've seen. Is that a personal observation, or is it from a passage in the book that I overlooked?

[y_feldblum]

It is both. The author mentions it, and it is in fact the way I have always done trigonometry. That is the way I was taught to do trigonometry.

From Chapter 1 page 17, posted online, "One can simulate rational trigonometry from within classical trigonometry, essentially by never calculating angles."

In other words, where one is not allowed to calculate angles, one is forced to use the methods of rational trigonometry. This is so whether one writes equations in terms of sines and cosines of angles, or in terms of spreads and crosses of lines [vectors]. One way obfuscates the method of solving problems; the other clarifies it.

[Felix]

Wow. Seems like my hopes were justified. I have to get that book.

[Quantum Mechanic]

For those that may have noticed, the spread between 2 lines is simply the square of the sine of the angle between them. So as y_feldblum states, classical trig is using rational trig implicitly.

Oh and Franklin, your response is one of the most unscientific and intellectually dishonest things I've ever read. Read the first chapter before making such jaw-dropping [ingly inccorect] comments.