Final answer:
Y can be determined using the Pythagorean theorem applied to the unit circle. With x=5/8, after solving, y equals ± the square root of 39/64, where the correct answer is b) √39/64, representing the positive root.
Step-by-step explanation:
If x=5/8 on the unit circle, the value of y can be determined using the Pythagorean theorem, which in the context of the unit circle is represented as x² + y² = 1 since the radius of the unit circle is 1. Given x=5/8, we plug this value into the equation to get (5/8)² + y² = 1. Squaring 5/8 gives us 25/64, thus the equation becomes 25/64 + y² = 1. To find y², we subtract 25/64 from both sides, yielding y² = 1 - 25/64 = 39/64. Finally, we take the square root of both sides to find the value of y, remembering we can have both positive and negative roots since the unit circle spans all four quadrants.
The calculations give us y = ±√(39/64). We simplify the square root of the fraction by taking the square root of the numerator and the denominator separately to get y = ±√39/8. Therefore, the answer choices provided have to be assessed for which one matches our positive and negative root. The correct answer choice is b) √39/64, as this represents the positive root of y's value.