# Math Help - laws of cosines

1. ## 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!

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

2. 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!

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

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

Use the "Proof of the geometric interpretation"

3. 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!

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

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

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

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

$\sin{2x} = 2\sin{x}\cos{x}$.

4. 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

5. What about the projection formula??

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

6. Originally Posted by pyrosilver

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...

7. Originally Posted by pyrosilver

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

Vector projection - Wikipedia, the free encyclopedia

8. Are there more than one? We have a w = ( u dot v / u dot u ) times u

9. 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.

10. 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!

11. 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