From the given problem we have cos(x) = 1/3. Remember that in the right triangle XYZ, with the right angle at Z, by definition the cosine of an angle is equal to the length of the adjacent side divided by the length of the hypotenuse.
We should also note that this triangle follows the Pythagorean theorem since it is a right triangle. According to the theorem, the sum of the squares of the lengths of the two legs of a right triangle is equal to the square of the length of the hypotenuse. In terms the of cosines, this can be expressed as cos²(x) + cos²(y) = 1. We can use this to express cos²(y) as 1 - cos²(x).
By substituting cos(x) = 1/3 into it, we get
cos²(y) = 1 - (1/3)²
cos²(y) = 1 - 1/9
cos²(y) = 8/9
Taking into account that the cosine of any angle is always between -1 and 1, we can conclude that cos(y) is the positive square root of cos²(y), since the cosine of an angle in a right triangle is always positive.
So, we have:
cos(y) = sqrt(8/9)
cos(y) ≈ 0.9428090415820634
Therefore, the correct answer is that none of the given options (1/3, 3, 1, 2/3) matches the approximately calculated value of cos(y).