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Find the solutions of the equation 2sin(x) + √3 = 0.
Find the solutions of the equation 2sin(x) + √3 = 0.
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Practice Questions
1 question
Q1
Find the solutions of the equation 2sin(x) + √3 = 0.
x = 5π/6
x = 7π/6
x = π/6
x = 11π/6
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Solving gives sin(x) = -√3/2, so x = 7π/6 and 11π/6.
Questions & Step-by-step Solutions
1 item
Q
Q: Find the solutions of the equation 2sin(x) + √3 = 0.
Solution:
Solving gives sin(x) = -√3/2, so x = 7π/6 and 11π/6.
Steps: 6
Show Steps
Step 1: Start with the equation 2sin(x) + √3 = 0.
Step 2: Isolate sin(x) by subtracting √3 from both sides: 2sin(x) = -√3.
Step 3: Divide both sides by 2 to solve for sin(x): sin(x) = -√3/2.
Step 4: Identify the angles where sin(x) equals -√3/2. These angles are in the third and fourth quadrants.
Step 5: The angles that satisfy sin(x) = -√3/2 are x = 7π/6 and x = 11π/6.
Step 6: Therefore, the solutions to the equation are x = 7π/6 and x = 11π/6.
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