Conics Help!!!! (1 Viewer)

[simonkey]

How come:

b(sinA - sinB) / a(cosA - cos B) =
(b/a) * 2sin(a-b / 2)cos(a+b / 2) / -2sin(a-b / 2) sin(a+b / 2)

This is the proof for the gradient of an ellipse in the Cambridge 4 unit book.

help me plzzz

 

[Riviet]

It's just using the sum of differences to products formulae which is not in the syllabus anymore.

See the top of page 2 of this.

 

[simonkey]

OHHHHHHHHHHHH!!!!!!!!!!!!!!!!!!!

Thank you for the help smart people. How do you derive the "sum or differences to products" ??

Thank you.

 

[Slidey]

Hey simon, just a word: don't delete your threads after you've made them, simply because somebody answered your question. It's better if they are left for others to read, as they may help them, too.

Now, onto your question:
You are aware of how to derive the following formula, right?
2sin(A)cos(B) = sin(A-B)+sin(A+B)
It's done by:
sin(A+B)=sinAcosB+cosAsinB
sin(A-B)=sinAcosB-cosAsinB
Add these:
sin(A+B)+sin(A-B) = 2sinAcosB

Ok, that's the easy bit. Now you should make a substitution:
Let A=(a+b)/2, B=(a-b)/2
You can see that A+B=a, A-B=b.
Thus we have:
sin(A+B)+sin(A-B) = 2sinAcosB
sin(a)+sin(b) = 2sin([a+b]/2)cos([a-b]/2)

That is to say: the two identities are equivalent in what they mean.

EDIT: lol found a typo a few days late

 

[simonkey]

Ohhhh!! Thanx for the help Slidey, it really helps. I deleted the threads cos no1 had replied yet and i didn't think any1 was ever going to.

 

[pLuvia]

Slidey, I'm a bit intrigued... What happened to your orange-ness? Or is it optionally disabled?

He resigned from being moderator

 

[pLuvia]

Yep

 

[haque]

pLuvia is a good strict moderator-but is it a lot of work?As in won't it hamper ur studies and free time?Sorry for my ignorance

 

[pLuvia]

Well not yet, but not as much conflict occurs in the maths forums as other forums

 

[Riviet]

They're mostly just threads with specific maths problems/queries and people answering them.

 

[pLuvia]

Pretty much but you can get the occasional idiotic/spammish threads which is reported quite fast anyway making my job easier

 

[Slidey]

Ohhhh!! Thanx for the help Slidey, it really helps. I deleted the threads cos no1 had replied yet and i didn't think any1 was ever going to.

No problem. Good luck!

Slidey, I'm a bit intrigued... What happened to your orange-ness? Or is it optionally disabled?

I'm no longer a member of the moderator body; I resigned for certain reasons. Besides, how often was I around this year? It was just time, I guess.

The maths forums, especially 4u, are the best forums on this board. People don't fight, the worst the trolls get is "I'm the smartest person in this forum!", and for the average thread, at least 3 people will attempt to help a person out within a day of the thread being posted. It's quite cool.

I'm not leaving, though, don't worry.