Solving problems using Half Angle identities

1. Nov 19, 2008

saychanh

1. The problem statement, all variables and given/known data

Solve for x using half-angle identities

cos (x/2) = -√2 / 2

2. Relevant equations

cos(x/2) = ± √(1+cosx)/2

3. 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?

Last edited: Nov 19, 2008
2. Nov 19, 2008

HallsofIvy

Staff Emeritus
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.

3. Nov 19, 2008

saychanh

Thank you so much

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