Solve the equation sin(x) = 0.5 for x in the interval [0, 2π].
Correct Answer: x = π/6 and x = 5π/6
- Step 1: Understand the equation sin(x) = 0.5. We need to find the values of x where the sine of x equals 0.5.
- Step 2: Recall the unit circle and the values of sine for common angles. The sine of an angle is 0.5 at specific angles.
- Step 3: Identify the angles where sin(x) = 0.5. These angles are π/6 and 5π/6.
- Step 4: Check if these angles are within the interval [0, 2π]. Both π/6 and 5π/6 are within this interval.
- Step 5: Write down the solutions. The solutions to the equation sin(x) = 0.5 in the interval [0, 2π] are x = π/6 and x = 5π/6.
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