what is sec and cot when sin = -2/5

This is either a 3rd or 4th quadrant angle.....

And sine = y/r  .....we need to find x

x = [ plus/minus] sqrt (5^2 -2^2) =  [plus / minus]sqrt(21)

sec = r/x  =  (plus/ minus)5/sqrt(21)

cot = x/y  = (plus/ minus) sqrt(21) / 2