trig problem??

Question

Let cos alpha - (sqroot 5) / 5: 0 < alpha < pi/2; sin beta = -4/5: -pi/2 < beta < 0. Find the exact value of the following:


c) sin (alpha / 2)

d) cos(2 beta)

please help and explain, keep getting different answers, thanks

Answer 1

Hmm. Better re-ask the first one, since you obviously made some sort of typo.

For the second, sin B = -4/5. Cos 2B is positive because of the range you're given for B -- but you actually don't need that fact. Just use cos 2B = 1 - 2 sin^2 B and you're done.