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[Vector]

I'd learn what you have to know about the geometric version, and then do some research into power series.  If you do that, you should probably be able to get the grasp you need on the material.

[Darvi]

Stuff like

2*sin^2(x)=1-cos(2x)

?

[Leafsnail]

You want to prove that?  Or just throwing it out there?

[Darvi]

Eh, it's easy. Unless you'd also want me to prove that cos(2x)=cos^2(x)-sin^2(x),' cuz that would take a while and perhaps a graph too.

Otherwise: 1= cos^2(x)+sin^2(x)

=>1-cos(2x) = cos^2(x)+sin^2(x) -[cos^2(x)-sin^2(x)] = 2*sin^2(x) 

[Zrk2]

Hey! I can do this stuff! Mostly just show the formulas and say 'Because the formulas say so.' Then show them how it's basically simple algebra with special ratios thrown in there.

Remember to remind them to always switch tan to sin/cos.

[Leafsnail]

Depends whether you want it to come out as tan or not.

[Darvi]

This is nice.

[Christes]

I just let my students use a 3x5 inch index card on the exams.  Memorizing all of the formulas is supremely pointless IMHO.  (Of course, then I can write problems to test if they really understand the formulas)

Eh, it's easy. Unless you'd also want me to prove that cos(2x)=cos^2(x)-sin^2(x),' cuz that would take a while and perhaps a graph too.

The real slight of hand here is proving it, but only doing so for acute angles.  That seems pretty standard. 

[ZetaX]

So, what can anybody here tell me about the Taniyama-Shimura-conjecture?

edit: ooh, trig.

It's equivalent to Fermat's Last Theorem and has to do with elliptic curves.

Not equivalent, but stronger. FLT followed from a special case the rest of TSC was settled after that.

[Vector]

Huh, really?  The article I read said that they were equivalent... perhaps it meant a stronger version of FLT, as I heard somewhere that the original was rather more manageable than the version we ended up with.

[Darvi]

They are closely related to each other. Proving one would mean proving the other. Which apparently eventually happened.

[MaximumZero]

I really need to stop reading the forums backward. For a second there, I thought you guys were talking about Faster Than Light travel. *sigh*

[Leafsnail]

I just let my students use a 3x5 inch index card on the exams.  Memorizing all of the formulas is supremely pointless IMHO.  (Of course, then I can write problems to test if they really understand the formulas)

We have something like this, although we're expected to remember the really basic ones.

[ZetaX]

Huh, really?  The article I read said that they were equivalent... perhaps it meant a stronger version of FLT, as I heard somewhere that the original was rather more manageable than the version we ended up with.

The original FLT follows from a special case as do some generalisations.
See http://en.wikipedia.org/wiki/Modularity_theorem .

[ZetaX]

I just let my students use a 3x5 inch index card on the exams.  Memorizing all of the formulas is supremely pointless IMHO.  (Of course, then I can write problems to test if they really understand the formulas)

Eh, it's easy. Unless you'd also want me to prove that cos(2x)=cos^2(x)-sin^2(x),' cuz that would take a while and perhaps a graph too.

The real slight of hand here is proving it, but only doing so for acute angles.  That seems pretty standard.

The one best way of proving and memorizing stupid trig. stuff is via e^(ix) = cos(x)+i·sin(x) and e^(x+y) = e^x · e^y. The trig. formulas are then just properties if real and imaginary parts.