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# de moivre's theorem watch

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1. Show using de moivres theorem

sin^4x = 1/8 cos(4x) - 1/2 cos(2x) + 3/8

hint given: let z = e^ix, then sinx = 1/(2i)(z-1/z) and cos(nx) = 1/2(z^n + 1/z^n)

I have replaced the character theta in the question with x because i dont have a theta symbol. If anyone could help me understand why sinx = 1/(2i)(z-1/z) when z = e^ix it would be much appreciated.

Sorry for the sloppy layout. Pls help, thnx
2. If

what is ? (Use binomial expansion) Noting that
3. I dont understand how if let z = e^ix, then sinx = 1/(2i)(z-1/z)

also, are u sure that sinx = (z-1/z)/2i, because i got confused by the mathematical expression, i thought it meant 1/[2i(z-1/z)]. thnx for helping me
4. you know e^ix = cosx + isinx, and e^-ix = cosx - isinx. so work it out...
5. I'm quite sure

I thought that was knowledge you knew?

Also

Do you know where to go from what ive said to you ?
6. I see it now, thanks so much guys. Im very rusty with the matsh right now, but im getting there
7. No probs if you have any other problems dont hesistate to ask.

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Updated: August 7, 2007
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