For an angle θ with the point (16, −30) on its terminating side, what is the value of cosine?

First, you will need to chart this out. Draw an x-y graph. Draw a right triangle in the fourth quadrant (because the pair is (16, -30) you move along x 16 spaces then down y for 30).

Second, label the bottom of the triangle 16 and the side of the triangle -30. Place theta in the corner closest to point (0,0). 

Third, find the hypontenuse using the formula a^2 + b^2 = c^2. Place 16 as "a" and -30 as "b". You should get 1156. Square root 1156 to get 34. 

Now find cosine based on theta's placement. You should get 16/34 (reduce this to 8/17) because cosine follows CAH (cosine = adjacent/hypotenuse)