express sin x/2 in terms of cos x
I have the answer, but how would you approach this problem?
Thanks.
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 $\displaystyle \theta = \frac x2$, 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)