Find cos ( u /2 ) if cos u = − 0.209 and u is in Quadrant-II. cos ( u /2 ) =?

Answer 1

cos(u/2) = ±√[(1 + cosu) / 2]

Since u is in quadrant 2, 90° < u < 180°. So, 45° < u/2 < 90°.

Therefore, u/2 lies in quadrant 1, cos(u/2) > 0.

cos(u/2) = √[(1 + cosu)/2] = √[(1 - 0.209)/2] = 0.629