Final answer:
The equation sin2x = √3/2 has solutions 30° and 150° when looking at the positive sine values in the first and second quadrants and dividing by 2 to solve for x.
Step-by-step explanation:
To solve the equation sin2x = √3/2, we must find the angles for which the sine is √3/2. In the unit circle, the sine values are positive in the first and second quadrants. The reference angle for √3/2 is 60° or π/3 radians since sin(60°) = √3/2. Therefore, the solutions for 2x in the interval [0°, 360°) are 120° and 60° (since we're looking for sin2x, we have to divide these angles by 2).
The correct solutions of sin2x = √3/2 are therefore 30° and 60° after dividing the aforementioned solutions by 2, giving us x = 30° / 2 = 15° and x = 60° / 2 = 30°. However, these solutions don't fit into the provided options, so let's look at the possible options again. We also need to consider the solutions in other quadrants for 2x, which leads us to 120° and 240°, as sine is also positive in the second quadrant. As a result, the second solution is 2x = 240°. Divide this by 2 to find x, which will give us 120°.
Hence, the correct answers from the options given would be 30° and 150°.