Step 1 :The point P is on the unit circle, which means it satisfies the equation \(x^2 + y^2 = 1\).
Step 2 :We know the y-coordinate of P is \(\frac{2}{3}\), and we need to find the x-coordinate.
Step 3 :Since P is in quadrant II, the x-coordinate should be negative.
Step 4 :We can substitute \(y = \frac{2}{3}\) into the equation of the unit circle to solve for x.
Step 5 :After substituting and solving, we find that \(x = -0.7453559924999299\).
Step 6 :Rounding to three decimal places, we get \(x = -0.745\).
Step 7 :Final Answer: The x-coordinate of point P is \(\boxed{-0.745}\).