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If sin(x) = 1/2, what are the possible values of x in the interval [0, 2π)?

Practice Questions

Q1
If sin(x) = 1/2, what are the possible values of x in the interval [0, 2π)?
  1. π/6, 5π/6
  2. π/4, 3π/4
  3. π/3, 2π/3
  4. 0, π

Questions & Step-by-Step Solutions

If sin(x) = 1/2, what are the possible values of x in the interval [0, 2π)?
  • Step 1: Understand that sin(x) = 1/2 means we are looking for angles 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(π/6) = 1/2. This is one angle we are looking for.
  • Step 4: Check the second quadrant where sine is also positive. The angle that gives sin(x) = 1/2 in the second quadrant is 5π/6.
  • Step 5: List the angles found: x = π/6 and x = 5π/6.
  • Step 6: Confirm that both angles are within the interval [0, 2π).
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