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

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

Options:

Correct Answer: π/6

Solution:

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

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

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.

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].