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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]?
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Practice Questions
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Q1
If sin(x) = 1/2, what is the value of x in the interval [0, 2π]?
π/6
5π/6
7π/6
11π/6
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The angles where sin(x) = 1/2 in the interval [0, 2π] are x = π/6 and x = 5π/6.
Questions & Step-by-step Solutions
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Q
Q: If sin(x) = 1/2, what is the value of x in the interval [0, 2π]?
Solution:
The angles where sin(x) = 1/2 in the interval [0, 2π] are x = π/6 and x = 5π/6.
Steps: 7
Show Steps
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.
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