Final answer:
To find sin 0 given cos 0 and the quadrant of 0, we can use the Pythagorean identity sin²θ + cos²θ = 1. Given cos 0 = 2/3 and the terminal side of 0 lies in quadrant IV, we can solve for sin 0 as √(5/9).
Step-by-step explanation:
To find sin 0, we can use the Pythagorean identity sin²θ + cos²θ = 1.
Given that cos 0 = 2/3 and the terminal side of 0 lies in quadrant IV, we know that the cosine is positive.
Using the Pythagorean identity, we can solve for sin 0:
sin²0 + (2/3)² = 1
sin²0 + 4/9 = 1
sin²0 = 5/9
sin 0 = ±√(5/9)
Since the terminal side of 0 lies in quadrant IV, we take the positive root:
sin 0 = √(5/9)