Question

If sin theta = (sqrt 3)/2, which could not be the value of theta? A. 60 degrees B. 120 degrees C. 240 degrees D. 420 degrees I know that the solutions for theta are pi/3 and 2pi/3, but how does that correlate?

Answer 1

Your are right, $\pi /3$ and 2$\pi /3$ are solutions.
Of course each of these solutions can be replaced by the same number +k2$\pi$ (with k being an element of Z) since sin x=sin (x+k2$\pi$) with k being an element of Z. 
Those are angle measures expressed in radians.
If you translate in degrees you basically have to know that  $\pi$ radian=180 degrees
so $\pi /3$ radian=60 degrees and 2$\pi /3$=120 degrees. So this two could be values of theta (A and B).
On top of that $\pi /3+2 \pi$ could also be a solution (x+k2$\pi$ with k=1). This can be translated to 60+360=420 degrees which is solution D.
So C. 240 degrees is the only one that could not be a value of theta.