how do i solve this equation for cos(beta/2)?

Question

cos(beta) = -sqrt 2 / sqrt 3, pi/2 < beta < pi therefore making it lie in quadrant 2.

cos(beta/2)= +/- sqrt (1 + cos(beta)) / (2)

i know i have to plug in the numbers and find a common denominator, in the end i got...

sqrt (sqrt 3 + - sqrt 2) / (2 sqrt 3)

but how do find out if it's suppose to be a positive or negative answer? thanks for the help.

Answer 1

GIVEN:
pi/2 < beta < pi

Divide each by 2

pi/4 < beta/2 < pi/2

So (beta/2) lies in first quadrant
All values of sin, cos, tan, etc. will be POSITIVE

Answer 2

the answer should be positive. since beta lies between pi/2 and pi, beta/2 lies between pi/4 and pi/2, making it in quadrant 1. cosine values in quadrant 1 are all positive