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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]?
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Practice Questions
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Q1
If sin(x) = 1/2, what is the value of x in the range [0, 2π]?
π/6
π/3
5π/6
7π/6
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x = π/6 and 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 range [0, 2π]?
Solution:
x = π/6 and 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 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.
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