Being able to do this problem hinges mainly on your knowing the definitions of the trig functions and being able to read side lengths from the given diagram.
csc theta = hypotenuse / opp side = 4 / √(4^2 + 5^2) = 4 / √41.
sin theta is the reciprocal of csc theta, or √41 / 4.
cot theta is adj side / opp side = 5/4.
