Well, the cos(∅) is negative in the second and third quadrants. If you are solving for theta, you would use the inverse of the cos or arccos [tex]cos(x) = ( \frac{-2}{3} )[/tex] take the inverse of both sides to get: x = arccos(-2/3) now evaluate the right x = 131.8103149 degrees to find your second solution, subtract your reference angle from 360 degrees. 360 - 131.8103149 = 228.1896851 degrees
Now the period of cos is 2π or 360 degrees. So if you want to consider all possible solutions, you would need to add/subtract 360n to both solutions above..
Not sure if this is what you're looking for, but thought I would leave it here for you just in case... As a side note, you could do this problem in radian measurement as well.
