half angle formulas?

Question

given cosx= -3/7 and pi/2

Answer 1

yes.
double and half angle formulas

cos(2t) = 2 cos(t)^2 -1 ...(double angle formula)
2t = x
t = x/2
cos(x) = 2 cos(x/2)^2 -1
2 cos(x/2)^2 = cos(x) +1
cos(x/2)^2 = ( cos(x) +1)/2

now
cos(x) = -(3/7)
then

cos(x/2)^2 = (-(3/7)+1)/2 = 2/7

pi/2 < x < pi
pi/4 < x/2 < pi/2
so...
cos(x/2) > 0

cos(x/2) = (2/7)^(1/2)

Answer 2

Given cosx = -3/7 and π/2 < x < π, find cos(x/2).

Since x is in the second quadrant, x/2 is in the first quadrant where cos(x/2) will be positive.

cos(x/2) = √[(1 + cosx)/2] = √[(1 - 3/7)/2] = √(2/7)