The negative coordinates -4 and -3 tell us that the terminal side of this angle theta lies in Quadrant III. The hypotenuse is sqrt( [-4]^2 + [-5]^2 ), or +5.
Then:
sin theta = opp / hyp = -3/5
cos theta = adj / hyp = -4/5
tan theta = opp / adj = (-3) / (-4) = 3/4
cot theta = adj / opp = 4/3
sec theta = hyp / adj = -5/4
csc theta = hyp / opp = -5/3
