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Prove:
cos θ = [ e^(iθ) + e^(-iθ) ] / 2
sin θ = [ e^(iθ) - e^(-iθ) ] / 2i

I already know that cis θ = e^(iθ)

And that:
cos θ = Re{ cis θ } = Re{ e^(iθ) }
sin θ = Im{ cis θ } = Im{ e^(iθ) }

But how do I actually extract the functions, in terms of e, of each trigonometric function?

How do I prove:
cos θ = [ e^(iθ) + e^(-iθ) ] / 2
sin θ = [ e^(iθ) - e^(-iθ) ] / 2i

2007-09-08 01:05:36 · 2 answers · asked by Anonymous in Mathematics

Today the seventh ODI is in progress

2007-09-08 01:05:31 · 12 answers · asked by Anonymous in Cricket

USSR seperated from its states after the war with afghanistan during the 70's. Do you think same will happen to the US?

2007-09-08 01:05:00 · 4 answers · asked by mnsrzafar 1 in Law & Ethics

who have the information that can tell me?

2007-09-08 01:04:57 · 1 answers · asked by fakejan 1 in Other - Careers & Employment

Like the history foretold by the books, I never knew the reason why the emperor of Japan desire the entire Asian countries for his own gain? What is exactly he is looking for-wealth? resources? Or was it his general's that advice him to conquer the countries within Asia minor then proceed to the US mainland?

2007-09-08 01:04:10 · 11 answers · asked by Anonymous in Military

A woman dies without a will. The only living relatives she had is one brother, and neices and nephews from both living and dead siblings. The one living brother dies before her estate is handled. She lived in New York.

2007-09-08 01:04:04 · 5 answers · asked by dlg54321 1 in Law & Ethics

It appears that both Bush's have had problems with disasters...why?....

2007-09-08 01:03:55 · 5 answers · asked by bruce b 3 in Other - Politics & Government

For the bathroom sink. I tried this pro stuff and it didn't seem much better.

2007-09-08 01:03:48 · 5 answers · asked by Bill Spry 4 in Maintenance & Repairs

Today the seventh ODI is in progress

2007-09-08 01:03:43 · 8 answers · asked by Anonymous in Cricket

2

Will moving a pup to an channel island make it poorly?? we sold a pup to a guy who lives on the channel island and he emailed me saying it's really poorly and it might not make it??
It had a clean bill of health when we had it, and all the other pup's are ok.
my dog had a litter of 8 and all the other seem to be fine.
He wants to us to pay all vet bill's what do we do?

2007-09-08 01:03:37 · 11 answers · asked by paula h 2 in Dogs

2007-09-08 01:02:45 · 10 answers · asked by Anonymous in Weather

0

Where does acid rain commonly occurs in the world?

2007-09-08 01:01:19 · 5 answers · asked by Anonymous in Weather

2007-09-08 01:00:42 · 19 answers · asked by Anonymous in NASCAR

I know this may look funny and non-sense to many. But I really have tough time in addressing my testing equipments by their brand name and model number. I need ur help in naming them in a simple way those can be understood globally. I have given the eqpments below. Pls give me some names those matches the letters.

V series (6 machines)

PK series (3 machines)

D series (2 machines)

M series (2 machines)

T series (5 machines)

E series (2 machines)

S series (4 machines)
------------------------------
One sample for ur reference: using the solar system
V = Venus

D = Dione

T= Titan

P = Pluto

M = Mars

E = Earth

S = Saturn
This looked interesting. But I wud appreciate if someone can gimme a better list....

Really THIS IS NO JOKE !

2007-09-08 01:00:21 · 2 answers · asked by Anonymous in Engineering

trying to purchase a bike this week for $9000 and will pay off the credit card when my equity loan goes through.

2007-09-08 01:00:09 · 6 answers · asked by reevesmreeves 1 in Credit

God Bless America and GWB.

2007-09-08 01:00:04 · 11 answers · asked by Anonymous in Politics

I had a greendot debit card and actived it April 4 2007. Reloaded it on April 24 and April 30, 2007( totaling 560.00). On May 8th 2007 I revieved an invoice from UPS that I hipped 3 packes and I was beeing invoice from my account. I have never used ups or ever in my life shipped anything corss country to anyone. reson being my entire family lives in San Francisco. To get to the problem my debit card was tapped in to and all my money was taken. Now Green Dot refuses to help or even investage the thift. Now there is a person in the ups fraud dept. that has been most helpful. I then called greendot and they told me to write a letter with suspect info. I then got a reply to the fact I was S.H.O.L. It was determined that i had an account with UPS. Ah! Daa!. I called greendot sopke to Dorthy (with no last name.it was not nessairy she said) who said exclatly what the reply did. They have no intention of doing anything. so now I was advised to take them to small claims court. help? anyone

2007-09-08 00:59:33 · 5 answers · asked by mugsy 1 in Law & Ethics

I am going to a all girls fancy dress party, i was the only boy invitied and i was asked by my best mate to come,i am well nervous about going, but i am also well excited too, but i have come across a promblem what do i wear?? pls help

2007-09-08 00:59:25 · 16 answers · asked by red25 1 in Halloween

Is it a signature conservative failure?...I stole this from Utube before anyone tells me..and of curse I am a liberal.

2007-09-08 00:58:57 · 11 answers · asked by bruce b 3 in Government

2007-09-08 00:58:27 · 14 answers · asked by lilac 7 in Polls & Surveys

Well, today is my first soccer game and we only had 1 practice. But, I haven't played since I was 8 years old everyone else on my time has played for along time.So, I don't want to go till i go through a couple more practices. Can you guys help to think of a way to make my parents not take me please!! I also don't know any of the positions.... otherwise I'm really good at soccer.

2007-09-08 00:58:05 · 9 answers · asked by Amber Lynn <3 3 in Other - Football

please explain these lines...


1.) praised be my lord for our sister, the death of the body, from whom no man escape

2.) woe to him who dieth in mortal sin!

3.) blessed are they who are found walking by the most holy will, for the second death shall have no power to do them harm


please...

POINTS WAITING.....

2007-09-08 00:57:47 · 9 answers · asked by Anonymous in Religion & Spirituality

i was doing a head check and when i looked back ahead of me my body had just gone ahead and changed lanes without me. whats happening there then?

2007-09-08 00:57:31 · 8 answers · asked by darkling 5 in Motorcycles

My sister´s daughter is Ella, named after my Grandmother. Since I like the name Eleanor too, should I name my daughter Ellie?

BTW, my sister´s other daughter is Lily.

2007-09-08 00:57:13 · 15 answers · asked by Learning is fun! 4 in Baby Names

hi, I have a problem around Wembley. On ‘event days’ I always get caught out on parking restrictions and I have received several tickets and have been towed a couple of times since the stadium has opened. Can I stick me banger car on anyones private driveway?

This would technical be free parking. What about event day. Why does everyone park in someone’s drive way?

2007-09-08 00:56:52 · 18 answers · asked by PUFFDADDYHEVEN 1 in Other - Cars & Transportation

If the fed drops interest rates will it not just prolong the agony and the level of debt before the recession finally hits. At least with boom and bust scenarios you can take stock of your situation and re-evaluate your own financial position. I will never forget the recession of the 1990 s, and new then I would never be so vulnerable again to fluctuations in the economy, I learned a valuable lessson. Does anyone have the same experiences as me.

2007-09-08 00:56:33 · 2 answers · asked by diablo.x 2 in Economics

I've got two, both named "Joshua"!

2007-09-08 00:55:41 · 30 answers · asked by Anonymous in Polls & Surveys

i hate my cousin khoa, she is ******* rude to me and she say stuff about me.And what can i do?I dont want to fight with her because i fight with her like a million times.She ask for my stuff and i say yah but when i ask her back she say no.She always tell me to do this and that.All the time what can i do???

2007-09-08 00:55:20 · 10 answers · asked by Anonymous in Family

If they do, do dey come off well after 4 years?
And how much do they cost?? And can I get dem at a normal tattoo place???
Thanks!

2007-09-08 00:54:17 · 7 answers · asked by Anonymous in Tattoos

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