Final answer:
The equation sin θ = 1/2 has solutions at θ = π/6 + 2kπ and θ = 5π/6 + 2kπ, where k is any integer and the angle is measured in radians.
Step-by-step explanation:
To solve the equation sin θ = 1/2, we need to find the values of θ for which the sine function returns a value of 1/2. Knowing that sin θ = 1/2 corresponds to the angles of 30 degrees (or π/6 rad) and 150 degrees (or 5π/6 rad), and considering the periodic nature of the sine function, we can write θ as:
- For the angle in the first quadrant: θ = π/6 + 2kπ, and
- For the angle in the second quadrant: θ = 5π/6 + 2kπ
where k is any integer. Since we want the answer in radians, we leave the known values of θ in terms of π. According to the question, answers should be rounded to two decimal places where appropriate, but since these specific answers are exact multiples of π, rounding is not required.