Final answer:
The coordinates of point P on the unit circle with a y-coordinate of -1/3 and a positive x-coordinate are (2√2/3, -1/3).
Step-by-step explanation:
To find the coordinates (x, y) of a point P on the unit circle, we can use the given information. In this case, we know that the y-coordinate of P is -1/3 and the x-coordinate is positive. Since the point lies on the unit circle, the distance from the origin to the point is 1. We can use the Pythagorean theorem to find the value of x:
x² + (-1/3)² = 1
x² + 1/9 = 1
x² = 1 - 1/9 = 8/9
x = ±√(8/9) = ±2√2/3
Since the x-coordinate is positive, we take the positive value: x = 2√2/3
Therefore, the coordinates of point P are (2√2/3, -1/3).