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

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

Options:

Correct Answer: π/6

Solution:

x = π/6 and 5π/6.

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

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.

Trigonometric Functions – Understanding the sine function and its values on the unit circle.
Inverse Trigonometric Functions – Using the inverse sine function to find angles corresponding to specific sine values.
Periodic Nature of Trigonometric Functions – Recognizing that sine is periodic and can have multiple solutions within a given range.