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

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

Options:

Correct Answer: π/6, 5π/6

Solution:

The angles where sin(x) = 1/2 are x = π/6 and x = 5π/6.

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

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).

Trigonometric Functions – Understanding the sine function and its values at specific angles.
Unit Circle – Using the unit circle to determine angles corresponding to specific sine values.
Interval Notation – Identifying solutions within a specified interval, in this case, [0, 2π).