Hi Kel,
If the angle is in the 4th quadrant, then cos of the angle must be positive so you can eliminate the first choice.
Since sin of the angle is -7/15, we can create a right triangle in the 4th quadrant with hypotuse equal to 15 and the vertical side (which is opposite the angle) equal to 7 (negative 7 really since we move downward.
Pythagorean Thm will help us find the horizontal side (which is adjacent to the angle).
7^2 + b^2 = 15^2
49 + b^2 = 225
b^2 = 176
b = 4sqrt11
So, the cosine of the angle is adjacent side divided by hypotenuse which is 4sqrt11/15 which is your second choice.
Hope this helps.
:)
