Which of the following is a solution to 2cos x + 1 = 0? 60° 120° 210° 300°

Rewrite   2cos x + 1 = 0    as:

2 cos x = -1, and then cos x = -1/2

x must be in Quadrant II or Quadrant III, since the adj. side is negative.

Note that the angle 120 has adj. side -1 and hyp 2.  So 120 degrees is one solution.  

Now what about a possible 2nd solution, to be found in Quadrant III?  That would be -120 degrees, which has the same terminal line as does 240 degrees.

No soap.

So, the solution is 120 degrees.

The answer is c. 7 (i think) i’m almost sure though