Question

If cosx=2/3 and x is in Q4, then sin(x/2)=?

Answer 1

do you know any identities that involve a half angle?

Answer 2

Yes

Answer 3

sin(x/2)=+/- sqrt((1-cosx)/2)

Answer 4

ok replace cos(x) with what is given

Answer 5

then follow order of operations
yes the same order of operations learned in beginning algebra

Answer 6

I'm lost in your first step... Replace what exactly with what?

Answer 7

cos(x)=2/3
so that tells me i can replace cos(x) with 2/3

Answer 8

let's see if he can get the answer

Answer 9

So...replacing cos(x) with 2/3, I am given sqrt((1-2/3)/2)

Is this correct so far?

Answer 10

and for prettiness i'm going to rewrite our identity
\[\sin(\frac{x}{2})=\pm \sqrt{\frac{1}{2}(1-\cos(x))} \\
\sin(\frac{x}{2})=\pm \sqrt{\frac{1}{2}(1-\frac{2}{3})}\]

Answer 11

now can you follow the order of operations to simplify this?

Answer 12

Yes, it's clear to me now.

Answer 13

Thank you so much!

Answer 14

+ or -sqrt((1-2/3)/2)
=+ or -sqrt((3-2/3)/2)
=+ or -1/sqrt (6)