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Find the solutions of the equation 2sin(x) - 1 = 0 in the interval [0, 2π].
Find the solutions of the equation 2sin(x) - 1 = 0 in the interval [0, 2π].
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Practice Questions
1 question
Q1
Find the solutions of the equation 2sin(x) - 1 = 0 in the interval [0, 2π].
π/6, 5π/6
π/4, 3π/4
π/3, 2π/3
π/2, 3π/2
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The solutions are x = π/6 and x = 5π/6.
Questions & Step-by-step Solutions
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Q
Q: Find the solutions of the equation 2sin(x) - 1 = 0 in the interval [0, 2π].
Solution:
The solutions are x = π/6 and x = 5π/6.
Steps: 6
Show Steps
Step 1: Start with the equation 2sin(x) - 1 = 0.
Step 2: Add 1 to both sides of the equation to isolate the sine term: 2sin(x) = 1.
Step 3: Divide both sides by 2 to solve for sin(x): sin(x) = 1/2.
Step 4: Identify the angles where sin(x) equals 1/2. These angles are in the unit circle.
Step 5: The angles that satisfy sin(x) = 1/2 in the interval [0, 2π] are x = π/6 and x = 5π/6.
Step 6: Therefore, the solutions to the equation in the given interval are x = π/6 and x = 5π/6.
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