Can someone find the positive and negative coterminal for this problem . 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.

fist on the left goes with the third on the right. second on the left goes with the fourth on the right. third on the left goes with the second on the right. the fourth on the left goes with first on the right