If sin(x) = 1/2, what are the possible values of x in [0, 2π]?
Correct Answer: π/6, 5π/6
- Step 1: Understand that we need to find the angle x where the sine value is 1/2.
- Step 2: Recall the unit circle and the values of sine for common angles.
- Step 3: Identify that sin(x) = 1/2 corresponds to specific angles in the unit circle.
- Step 4: The first angle where sin(x) = 1/2 is π/6 (30 degrees).
- Step 5: The second angle where sin(x) = 1/2 is 5π/6 (150 degrees).
- Step 6: Both angles π/6 and 5π/6 are within the interval [0, 2π].
- Step 7: Conclude that the possible values of x are π/6 and 5π/6.
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