If θ is in quadrant iii and sinθ = -3/5, then cosθ =

Because the angle omega is in QIII, the adjacent side lies to the left of the origin and thus is represented by a negative value.  Since sin omega = -3/5, the opposite side is also negative.  Use the Pythagorean Theorem to obtain the length of the adjacent side:  5^2 = (-3)^2 + x^2, or 25 = 9 + x^2, or x^2 = 16.

Solving for x:  x = plus or minus 4.  Since we are in QIII, let x = -4.

Then cos omega is  opp / hyp, or -4/5.