# Thread: express sin x/2 in terms of cos x

1. ## express 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.

2. Originally Posted by white_cap
express sin x/2 in terms of cos x

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

Thanks.
use the half angle formula. you know it right?

3. 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

So i'm assuming you can't do this with only the double angle formula?

4. Originally Posted by white_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

So i'm assuming you can't do this with only the double angle formula?
yes, there is a way to use double angles.

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

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

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

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