Help with Proof

Any math whizzes out there? Could you help me prove that:

Cos (pi/5) = (1 + square root of 5)/4

Note that the second expression is the quantity of one plus the square root of five divided by four (hence the parenthesis).

Much appreciated.

Im good at maths *Mumbles i lieing * Heh sorry no can do pal" ^_^

That's alright. This is a very hard proof.

Originally Posted by Eldin

Any math whizzes out there? Could you help me prove that:

Cos (pi/5) = (1 + square root of 5)/4

Note that the second expression is the quantity of one plus the square root of five divided by four (hence the parenthesis).

Much appreciated.

You found someone!
Okay, gimme a minute...

?
I'm writing it out, and it looks wierd.
Are you allowed to graph or anything like that?

GOT-told you he's clever

Umm yeah i only posted to get first post,YAY.Im good at jokes people

It's hard writing out the problem with the symbols on a keyboard.

Trust me. The equation is valid. I checked on my calculator. The goal is to get one side to equal the other by using various identities. I don't even know where to start, though.

Originally Posted by Eldin

It's hard writing out the problem with the symbols on a keyboard.

Trust me. The equation is valid. I checked on my calculator. The goal is to get one side to equal the other by using various identities. I don't even know where to start, though.

Various identities?
I didnt really see anything that could use them.

The only thing I could do was change cos(pi/5) to cos36 degrees...
I'm not really sure what to do with the other side.
(I'm not even sure if changing from Radians to Degrees will do anything)

Cos (pi/5) = (1 + square root of 5)/4

CosXpie and CosX5= (I do not know) and (I do not know).
(I do not know)/(I do not know)=.25+2.23606798/4
(I do not know)/(I do not know)=.25+.559016995

I might of done it wrong, I don't know. Thats as far as I can go.

Originally Posted by Zelda Ninja

Cos (pi/5) = (1 + square root of 5)/4

CosXpie and CosX5= (I do not know) and (I do not know).
(I do not know)/(I do not know)=.25+2.23606798/4
(I do not know)/(I do not know)=.25+.559016995

I might of done it wrong, I don't know. Thats as far as I can go.

That's not right...
You cant separate the (Pi/5)

Then would it be

(I do not know/I do not know) =.25+.559016995?

Actually both sides are supposed to equal .809016994

Eldin, could you give examples of other problems that need to be solved in the same way, and show how you solved them?

Okay Eldin, I'm not sure if you can do this, but:


What if you change cos(pi/5) to cos36 degrees.

Then you work the other side in order to get it's exact value, which is ~.80901

Next, you do the cos inverse of .80901, and you'll get cos36 degrees

Therefore, cos36=cos36.

- Will that work?

Originally Posted by God of Twilight

Actually both sides are supposed to equal .809016994

This is true. That's the value I got.

Eldin, could you give examples of other problems that need to be solved in the same way, and show how you solved them?

This is an extra credit problem. It is far more advanced then any of the other problems I've done.

Basically, we've used the pythagorean identity (sin 2* + cos 2 = 1) and its variants, reciprocal identities, angle addition identities and so on. The class this is for is Trigonometry.

*Where 2 actually means squared.

What if you change cos(pi/5) to cos36 degrees.

It doesn't matter if it is in radians or degrees.

Will that work?

It technically works, but I don't think that's exactly what he's looking for.

What identities have you learned so far, I only know up to half-angle, so I might be able to help.

GOT: when you do identities you have to work on only one side of the equation.

Originally Posted by God of Twilight

Okay Eldin, I'm not sure if you can do this, but:


What if you change cos(pi/5) to cos36 degrees.

Then you work the other side in order to get it's exact value, which is ~.80901

Next, you do the cos inverse of .80901, and you'll get cos36 degrees

Therefore, cos36=cos36.

- Will that work?

No.

Proofs won't work if you convert anything to a non-finite decimal number or if you try to convert an irrational number into a finite decimal.

Originally Posted by squall24

What identities have you learned so far, I only know up to half-angle, so I might be able to help.

GOT: when you do identities you have to work on only one side of the equation.

Actually you can do both.
(I would know, since I just did a chapter on identities last week)

Originally Posted by God of Twilight

Actually you can do both.
(I would know, since I just did a chapter on identities last week)

Maybe so, but it is best to work on one side only. Many teachers and professors want one side only proofs. It shows that you know how to do the steps fully. Trust me on this. My math professor told us about 75% of the math profs. on campus use the one side only approach.

Originally Posted by squall24

Maybe so, but it is best to work on one side only. Many teachers and professors want one side only proofs. It shows that you know how to do the steps fully. Trust me on this. My math professor told us about 75% of the math profs. on campus use the one side only approach.

I realize that, but all I said was you CAN do both sides.
Anyways, this isnt the point of the thread...

EDIT: phail

^Thanks. I figured we'd have to get those involved somewhere along the line. I'll take a closer look at this tomorrow to make sure it's right. If it is, I definitely owe you one.