cosine

mirela · **Joined:** Mon, 27 Feb 2012 21:04:13 UTC **Posts:** 5

Show that cos (3theta)=4cos^3(theta)-3cos(theta)

Shadow · **Posted:** Fri, 2 Mar 2012 02:11:31 UTC

mirela wrote:

Show that cos (3theta)=4cos^3(theta)-3cos(theta)

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

Voxx · **Posted:** Fri, 2 Mar 2012 16:48:57 UTC

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

Shadow · **Posted:** Fri, 2 Mar 2012 17:42:58 UTC

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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cosine

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