Final answer:
To find the value of x for the point on the unit circle, we substitute the given y-coordinate into the unit circle equation x² + y² = 1 and solve for x, yielding two possible values: ±2/3.
Step-by-step explanation:
The question is asking to find the value of x for the point p=(x, (sqrt(5))/3) that lies on the unit circle. The equation of a unit circle is x² + y² = 1. Substituting the given y-coordinate into this equation yields:
x² + ((sqrt(5))/3)² = 1
To simplify, we square the y-coordinate:
x² + (5/9) = 1
Then, isolating the x-coordinate, we get:
x² = 1 - (5/9)
x² = (9/9) - (5/9)
x² = 4/9
Taking the square root of both sides, we find that:
x = ±(2/3)
Since the unit circle consists of all points where the x-coordinate is less than or equal to 1 and greater than or equal to -1, x must be either 2/3 or -2/3. Without additional information about the quadrant, both solutions are valid.