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Solve the equation sin(x) = 0.5 for x in the interval [0, 2π].
Solve the equation sin(x) = 0.5 for x in the interval [0, 2π].
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Practice Questions
1 question
Q1
Solve the equation sin(x) = 0.5 for x in the interval [0, 2π].
π/6
5π/6
7π/6
11π/6
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The solutions are x = π/6 and x = 5π/6 in the interval [0, 2π].
Questions & Step-by-step Solutions
1 item
Q
Q: Solve the equation sin(x) = 0.5 for x in the interval [0, 2π].
Solution:
The solutions are x = π/6 and x = 5π/6 in the interval [0, 2π].
Steps: 5
Show Steps
Step 1: Understand the equation sin(x) = 0.5. We need to find the values of x where the sine of x equals 0.5.
Step 2: Recall the unit circle and the values of sine for common angles. The sine of an angle is 0.5 at specific angles.
Step 3: Identify the angles where sin(x) = 0.5. These angles are π/6 and 5π/6.
Step 4: Check if these angles are within the interval [0, 2π]. Both π/6 and 5π/6 are within this interval.
Step 5: Write down the solutions. The solutions to the equation sin(x) = 0.5 in the interval [0, 2π] are x = π/6 and x = 5π/6.
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