Can someone help find the positive and negative coterminal for this problem please. I got either the positive or negative one wrong but I keep getting the same answer separately for both.

Check the picture below.
let's notice that 89/36 => 2 and 17/36, namely 2π or two revolutions and then a bit more, the 17/36 slack, so then -89π/36 = - 2π - 17π/36.
the positive angle will of course be 2π - 17π/36 = 55π/36.