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If sin(x) = 1/2, what is the value of x in the interval [0, 2π]?

Practice Questions

Q1
If sin(x) = 1/2, what is the value of x in the interval [0, 2π]?
  1. π/6
  2. 5π/6
  3. 7π/6
  4. 11π/6

Questions & Step-by-Step Solutions

If sin(x) = 1/2, what is the value of x in the interval [0, 2π]?
  • Step 1: Understand that we are looking for angles x where the sine of x equals 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 values of x in the interval [0, 2π] are x = π/6 and x = 5π/6.
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