Final answer:
Three possible angles on the domain [0, ∞] given that the sine of θ is equal to √3/2 are 60 degrees, 180 degrees, and 300 degrees (or π/3, π, and 5π/3 radians, respectively).
Step-by-step explanation:
To determine three possible angles on the domain [0, ∞] given that the sine of θ is equal to √3/2, we can use the inverse sine function (arcsin or sin-1) to find the angles. The inverse sine function returns the angle whose sine is a given value. In this case, the inverse sine of √3/2 is 60 degrees or π/3 radians. Since the sine function has a periodicity of 2π, we can find two more angles by adding 2π to the initial angle. So the three possible angles are 60 degrees, 180 degrees, and 300 degrees (or π/3, π, and 5π/3 radians, respectively).