Angle x is a third quadrant angle such that cosx=−2/3 .
What is the exact value of cos(x/2) ?
Answer in simplest radical form
cos x = -2/3
Since x is in Q#, then (x/2) will lie in Q2 .....and the cosine is negative there....so.....
cos (x/2) = - √ [ (1 +cosx) /2 [ = - √ [ (1 - 2/3) /2 ] = - √ [ (3 - 2) / 6 ] = -√ (1/6) =
- √6 / 6
