Question

Given \cos(\alpha)=\frac{8}{9} and 0<\alpha<\pi/2, find the exact value of \hbox{} \cos(\alpha/2)

Answer 1

\( \cos(\alpha)=\frac{8}{9}\) and \(0<\alpha<\frac{\pi}{2}\) find the exact value of \(\cos(\frac{\alpha}{2})\)
just trying to make it legible

Answer 2

is that the question? if so, you need the "half angle" formula
do you know it?

Answer 3

yes

Answer 4

\[\cos(\frac{\alpha}{2})=\pm\sqrt{\frac{1+\cos(\alpha)}{2}}\] plug in \(\frac{8}{9}\) where you see \(\cos(\alpha)\) and you get it

Answer 5

oh also note that since you are in quadrant 1, doubling it will be in quadrant 2, so your cosine is positive i.e. ignore the \(\pm\) and just use \(+\)

Answer 6

so from there I just plug in the numberS? Thank you

Answer 7

yes, you might want to simplify the compound fraction inside the radical after you write \[\cos(\frac{\alpha}{2})=\sqrt{\frac{1+\frac{8}{9}}{2}}\]

Answer 8

I do not think I am getting the right answer..