express sin x/2 in terms of cos x

• Nov 15th 2007, 05:52 PM
white_cap
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.
• Nov 15th 2007, 06:27 PM
Jhevon
Quote:

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?
• Nov 15th 2007, 06:49 PM
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 :D

So i'm assuming you can't do this with only the double angle formula?
• Nov 15th 2007, 08:23 PM
Jhevon
Quote:

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 :D

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)