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

Practice Questions

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

Questions & Step-by-Step Solutions

If sin(x) = 1/2, what is the value of x in the range [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 solution.
  • Step 4: Since sine is positive in the first and second quadrants, find the second angle where sine is also 1/2.
  • Step 5: The second angle is found by using the reference angle π/6 in the second quadrant, which is 5π/6.
  • Step 6: Therefore, the two solutions for x in the range [0, 2π] are x = π/6 and x = 5π/6.
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