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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)?
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Practice Questions
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Q1
If sin(x) = 1/2, what are the possible values of x in the interval [0, 2π)?
π/6, 5π/6
π/4, 3π/4
π/3, 2π/3
0, π
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The angles where sin(x) = 1/2 are x = π/6 and x = 5π/6.
Questions & Step-by-step Solutions
1 item
Q
Q: If sin(x) = 1/2, what are the possible values of x in the interval [0, 2π)?
Solution:
The angles where sin(x) = 1/2 are x = π/6 and x = 5π/6.
Steps: 6
Show Steps
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).
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