You're question, from what I can gather, asks: What is the value of the cosine function in radians at -1/2 if the function has a range of [-1, 1] and a domain of 0 to Pi.
Take a look at the image below, Pi/2 occurs when y=0, and pi occurs when y= -1. Since we know that the point y=-1/2 lies between pi/2 and pi it cannot be pi/6 or pi/3. And radians are not negative since the domain is not between 0 and -pi. Therefore the answer has to be 2pi/3.
If you're in doubt try cos of 120° or cos of 2pi/3 in your calculator, you'll get the answer -0.5 or -1/2.