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trigonometry

Defines: 
sine,cosine,tangent,secant,cosecant,cotangent
Type of Math Object: 
Topic
Major Section: 
Reference

Mathematics Subject Classification

43-00 no label found51-00 no label found42-00 no label found33B10 no label found

Comments

to my surprise there wasn't an entry defining and dealing and defining the elementary trigonometric functions, so I went and created this.

I know this entry is the kind of entry that will generate a long thread about comments, suggestions criticism and all that jazz, so why don't someone better sets up an asteroidmeta page for this so we can avoid polluting the page (and making it a lot larger and slower to load ;)

It's incomplete as it stands right now, but I'm making it world editable so anyone can work on it directly. Ah, and I'd like it to keep it as real trig mostly entru, so please do not dwell too much into complex analysis (perhaps just some mention and references)
f
G -----> H G
p \ /_ ----- ~ f(G)
\ / f ker f
G/ker f

Actually, THERE IS already an entry defining elementary trigonometric functions:

http://planetmath.org/encyclopedia/DefinitionsInTrigonometry.html

Another entry defining geometrically the sine and cosine of all real numbers is

http://planetmath.org/encyclopedia/CyclometricFunctions.html.

does cyclometric functions one really defines them?
it seems a bit circular to me if you want them to define sin, cos, etc
(unless you use the power series at the bottom to define arcsin first and then define sin as the inverse of arcsin, but then it gets all too contrived)
f
G -----> H G
p \ /_ ----- ~ f(G)
\ / f ker f
G/ker f

The first section of your entry is a repeat of "definitions in trigonometry" and as a matter of fact the previous entry is a little clearer in the exposition (for my taste). And that entry defines (i.e. they are in the "also defines" list) sine, cosine and the kind.

I like the idea of extending the topic and adding a bunch of things that "defs in trig. " is missing though, that is why I suggested making your entry a child of that one.

Alvaro

Ok I'll attach it, but keep in mind I said the entry as it stands is far from complete, right now I'm redoing the picture so I can fill the correction you still have opened, and many other things need to be added
f
G -----> H G
p \ /_ ----- ~ f(G)
\ / f ker f
G/ker f

Thanks!

And again, thanks for adding this entry to the collection, I have also noticed that Planetmath was a little weak in trigonometry.

Alvaro

As I see it, there really should be both definitions available. The definition in terms of sides and angles is uitable for beginners studying geometry and the definition in terms of power series and invers functions is more suitable for more advanced people.

Hoewever, this discussion should never have happened here, so I am going to build the wiki so we can carry out the discussion in a more suitable place.

Please post all further discussion of this entry to the following webpage:

http://oddwiki.taoriver.net/wiki.pl/AsteroidMeta/Discussion_of_Trigonometry

Maybe, it seems a bit circular. In fact the 'defining' of sine and cosine (for all real numbers) is only a subplot in explaining the old names arcsin and arccos -- you will see it if you read anew the whole article. But possibly I shall improve the order of things there. - The power series here is not any definition of arcsin, but only a formula.

Jussi

all I pointed is that I can't see the cyclometric entry defining the trig functions, just making use of them
f
G -----> H G
p \ /_ ----- ~ f(G)
\ / f ker f
G/ker f

All right =o)

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