express sin x/2 in terms of cos x

I have the answer, but how would you approach this problem?

Thanks.

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- Nov 15th 2007, 04:52 PMwhite_capexpress sin x/2 in terms of cos x
express sin x/2 in terms of cos x

I have the answer, but how would you approach this problem?

Thanks. - Nov 15th 2007, 05:27 PMJhevon
- Nov 15th 2007, 05:49 PMwhite_cap
Is there a way to do this question using only double angle formulas? Our class has not done the half angle formula yet.

I googled the half angle formula, and it worked wonders. Thanks :D

So i'm assuming you can't do this with only the double angle formula? - Nov 15th 2007, 07:23 PMJhevon
yes, there is a way to use double angles.

Let $\displaystyle \theta = \frac x2$, so now the problem is to express $\displaystyle \sin \theta$ in terms of $\displaystyle \cos 2 \theta$

start with the double angle formula for cosine:

$\displaystyle \cos 2 \theta = 1 - 2 \sin^2 \theta$

now solve for $\displaystyle \sin \theta$, when you're finished, replace all the $\displaystyle \theta$'s with $\displaystyle \frac x2$ and viola! (you'll realize this is just the half angle formula. your sly professor just had you derive it yourself)