# laws of cosines

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• November 9th 2008, 06:56 PM
pyrosilver
laws of cosines
Okay I am FLIPPING OUT. I have a math test tomorrow. I have to go to bed in an hour, and I just now learned that I have to be able to derive three separate things!

Please help me. I am seriously distressed.

1. How do I derive the Law of Cosines, vector style? Okay here's what I have...the asterisk (*) means dot in this:

|u-v|^2 = |u|^2 + |v|^2 - 2|u||v|cos theta

(u-v)(u-v) = u * u + v * v - 2 |u||v|cos theta

Where do I go from there? How do I make cos theta equal u * v/ |u||v|??

2. Projection formula w = ( (u*v)/u*u ) u ???? How do I derive that?!?!?!!

3. Double angle formula, sinx = 2cosx sinx .... HOW DO I DO THAT...Here is my start:

h=cosx * w
x=sinx * w

PLEASE HELP my test is TOMORROW, if you guys can't help me I'm doomed
• November 9th 2008, 07:05 PM
Prove It
Quote:

Originally Posted by pyrosilver
Okay I am FLIPPING OUT. I have a math test tomorrow. I have to go to bed in an hour, and I just now learned that I have to be able to derive three separate things!

Please help me. I am seriously distressed.

1. How do I derive the Law of Cosines, vector style? Okay here's what I have...the asterisk (*) means dot in this:

|u-v|^2 = |u|^2 + |v|^2 - 2|u||v|cos theta

(u-v)(u-v) = u * u + v * v - 2 |u||v|cos theta

Where do I go from there? How do I make cos theta equal u * v/ |u||v|??

2. Projection formula w = ( (u*v)/u*u ) u ???? How do I derive that?!?!?!!

3. Double angle formula, sinx = 2cosx sinx .... HOW DO I DO THAT...Here is my start:

h=cosx * w
x=sinx * w

PLEASE HELP my test is TOMORROW, if you guys can't help me I'm doomed

For 1), Dot product - Wikipedia, the free encyclopedia

Use the "Proof of the geometric interpretation"
• November 9th 2008, 07:10 PM
Prove It
Quote:

Originally Posted by pyrosilver
Okay I am FLIPPING OUT. I have a math test tomorrow. I have to go to bed in an hour, and I just now learned that I have to be able to derive three separate things!

Please help me. I am seriously distressed.

1. How do I derive the Law of Cosines, vector style? Okay here's what I have...the asterisk (*) means dot in this:

|u-v|^2 = |u|^2 + |v|^2 - 2|u||v|cos theta

(u-v)(u-v) = u * u + v * v - 2 |u||v|cos theta

Where do I go from there? How do I make cos theta equal u * v/ |u||v|??

2. Projection formula w = ( (u*v)/u*u ) u ???? How do I derive that?!?!?!!

3. Double angle formula, sinx = 2cosx sinx .... HOW DO I DO THAT...Here is my start:

h=cosx * w
x=sinx * w

PLEASE HELP my test is TOMORROW, if you guys can't help me I'm doomed

3. $\sin{(\alpha + \beta)} = \sin{\alpha}\cos{\beta} + \cos{\alpha}\sin{\beta}$

If we let $\alpha = \beta = x$ we get

$\sin{(x + x)} = \sin{x}\cos{x} + \cos{x}\sin{x}$

$\sin{2x} = 2\sin{x}\cos{x}$.
• November 9th 2008, 07:19 PM
pyrosilver
Thank you so much, that helped immensely!

Can someone help mew ith the projection formula?

edit: didn't see you post, thank you so much, lemme go read it
• November 9th 2008, 07:33 PM
pyrosilver
What about the projection formula??

Thank you so much for your help so far prove it you are saving my life
• November 9th 2008, 07:36 PM
Prove It
Quote:

Originally Posted by pyrosilver
What about the projection formula??

Thank you so much for your help so far prove it you are saving my life

I don't know what the projection formula is asking for...
• November 9th 2008, 07:38 PM
Prove It
Quote:

Originally Posted by pyrosilver
What about the projection formula??

Thank you so much for your help so far prove it you are saving my life

Found it

Vector projection - Wikipedia, the free encyclopedia
• November 9th 2008, 07:48 PM
pyrosilver
Are there more than one? We have a w = ( u dot v / u dot u ) times u
• November 9th 2008, 07:53 PM
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Quote:

Originally Posted by pyrosilver
Are there more than one? We have a w = ( u dot v / u dot u ) times u

$u\cdot u = |u|^2$

So in the link, replace C with w, A with u and B with v.
• November 9th 2008, 08:15 PM
pyrosilver
That helped!

Prove It, I cannot thank you enough for your help. You are so kind -- thank you for spending so much time researching this and helping me. You are AMAZING. THANK YOU SO FREAKING MUCH!
• November 9th 2008, 08:30 PM
Prove It
Quote:

Originally Posted by pyrosilver
That helped!

Prove It, I cannot thank you enough for your help. You are so kind -- thank you for spending so much time researching this and helping me. You are AMAZING. THANK YOU SO FREAKING MUCH!

No problem. Just remember, if in doubt, check Wikipedia :P