Solving problems using Half Angle identities

[saychanh]

Homework Statement

Solve for x using half-angle identities

cos (x/2) = -√2 / 2

Homework Equations

cos(x/2) = ± √(1+cosx)/2

The Attempt at a Solution

I am trying to figure out what to do with the identity, but I have no idea how to start. I know that x = 270 degrees or 3pi/2, but I do not know how to get there. Can someone head me in the right direction?

 

[HallsofIvy]

cos²u= (1+ cos 2u)/2

Let u= x/2. Then $(1+ cos x)/2= (-\sqrt{2}/2)^2= 1/2$ so 1+ cos(x)= 0, cos(x)= -1.

 

[saychanh]

Thank you so much