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 Post subject: cosine
PostPosted: Fri, 2 Mar 2012 00:55:37 UTC 
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Joined: Mon, 27 Feb 2012 21:04:13 UTC
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Show that cos (3theta)=4cos^3(theta)-3cos(theta)


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 Post subject: Re: cosine
PostPosted: Fri, 2 Mar 2012 02:11:31 UTC 
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mirela wrote:
Show that cos (3theta)=4cos^3(theta)-3cos(theta)


e^{3i\theta}=\cos(3\theta)+i\sin(3\theta).

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 Post subject: Re: cosine
PostPosted: Fri, 2 Mar 2012 16:48:57 UTC 
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another way:

we know that:
1. cos(a+b) = cos(a).cos(b) - sen(a).sen(b)
2. cos(2theta) = cos^2(theta) - sin^2(theta)
3. cos(3theta)=cos(theta+2theta)

starting in 3., use 1., after this use 2. and use the relation sin^2(theta) = 1 - cos^2(theta)

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 Post subject: Re: cosine
PostPosted: Fri, 2 Mar 2012 17:42:58 UTC 
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Voxx wrote:
another way:

we know that:
1. cos(a+b) = cos(a).cos(b) - sen(a).sen(b)
2. cos(2theta) = cos^2(theta) - sin^2(theta)
3. cos(3theta)=cos(theta+2theta)

starting in 3., use 1., after this use 2. and use the relation sin^2(theta) = 1 - cos^2(theta)

Bye
Voxx


If you advocate this route, you should really use \cos(2\theta)=2\cos^2\theta-1

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