Final answer:
The correct solution set for sin(3x) = 1/2 is d. 7π/18, 11π/18, by finding the angles where the sine function equals 1/2 and dividing by 3 to solve for x within the interval [0, 2π).
Step-by-step explanation:
The student asked for the particular solution set of sin(3x) = 1/2. To find this, we first need to identify the angles for which the sine value is 1/2. Sine takes the value of 1/2 at π/6 and 5π/6 radians. Therefore, we look for angles within the form 3x = π/6 + k(2π) and 3x = 5π/6 + k(2π), where k is any integer. Dividing these expressions by 3 to solve for x gives us x = π/18 + k(2π/3) and x = 5π/18 + k(2π/3). The values of x that are within one period [0, 2π) and satisfy the equation sin(3x) = 1/2 are 5π/18, 7π/18, and 11π/18. Therefore, the correct answer is d. 7π/18, 11π/18.