Final answer:
To find the coordinate P(x, y) on the unit circle with a y-coordinate of -1/3 and a positive x-coordinate, you substitute y into the unit circle equation x² + y² = 1 and solve for x, resulting in P being (2√2 / 3, -1/3).
Step-by-step explanation:
The question involves finding the coordinates P(x, y) on the unit circle given that the y-coordinate is -1/3 and the x-coordinate is positive. The unit circle is defined by the equation x² + y² = 1. Since we know y is -1/3, we can substitute it into the unit circle equation to find x.
Doing the math:
- x² + (-1/3)² = 1
- x² + 1/9 = 1
- x² = 1 - 1/9
- x² = 8/9
- x = ±√(8/9)
Since the x-coordinate is positive, we only consider the positive square root:
- x = √(8/9)
- x = √8 / 3
- x = 2√2 / 3
Therefore, the coordinate P on the unit circle is (2√2 / 3, -1/3).