For this problem, we simply need to find the value of theta for which arcsin(-sqrt(2)/2) is true. This value is π/4 or 45 degrees if we had a positive. To make the negative true, we need the angle to be in the third or fourth quadrants (i.e., 5π/4 and 7π/4). These are two of the answer choices. And then anytime these return (i.e., by adding 8/4 to either of these) should also be selected as a correct angle. Thus we get 13π/4 as the final angle.
