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

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

Options:

  1. π/6, 5π/6
  2. π/4, 3π/4
  3. 0, π
  4. π/3, 2π/3

Correct Answer: π/6, 5π/6

Solution: 

sin(x) = 1/2 at x = π/6 and x = 5π/6 in the interval [0, 2π].

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

Practice Questions

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

Questions & Step-by-Step Solutions

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.
  • Trigonometric Functions – Understanding the sine function and its values on the unit circle.
  • Inverse Trigonometric Functions – Finding angles corresponding to specific sine values.
  • Periodic Nature of Trigonometric Functions – Recognizing that sine has multiple solutions within a given interval.
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