If sin(u) = - 4/5 with pi<x<3pi/2 what does cos(u/2) =?

If sin(u) = - 4/5 with π < u < 3π/2, what does cos(u/2) = ?

cos²(u) + sin²(u) = 1
cos²(u) + (-4/5)² = 1
cos²(u) + (16/25) = 1
cos²(u) = 1 - (16/25)
cos²(u) = 9/25
cos(u) = -√(9/25) for cos(u) < 0 when π < x < 3π/2
cos(u) = 3/5

cos(u) = 2 cos²(u/2) - 1
3/5 = 2 cos²(u/2) - 1
cos²(u/2) = (3/5) + 1
cos²(u/2) = 8/5
cos (u/2) = -√(8/5) for cos(u/2) when π/2 < u/2 < 3π/4
cos(u/2) = -2(√10)/5