Use the unit circle to find the inverse function value in degrees cos^-1 (sqrt3/2) 60 degrees 30 degrees 240 degrees 150 degrees

Better to write that as:

       -1
cos      [ sqrt(3) / 2 ]

since the cosine is defined as "adjacent side over hypotenuse,"  we know that the adj. side is sqrt(3) and that the hyp is 2.    The primary solution will be in Quadrant I because the adj. side is positive.

Think:  which angle in Q I has adj. side equal to sqrt(3) and hyp equal to 2?

That'd be 30 degrees.  Unfortunately, that's not one of your answer choices.  Thus, reflect that angle in the positive x-axis; you'll end up with a ray whose positive angle is 330 degrees. 

I'd suggest you ensure that you've copied this problem down correctly.
                                                                 sqrt(3)
Did you mean sqrt(3/2) or did you mean   ?? 
                                                                     2

Think of it as five or above give it a shove. change the 5 or above to the right to a zero and add one to the number on the left.