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Find the solutions of the equation 2sin(x) + √3 = 0.

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What’s inside this PDF?

Question: Find the solutions of the equation 2sin(x) + √3 = 0.

Options:

  1. x = 5π/6
  2. x = 7π/6
  3. x = π/6
  4. x = 11π/6

Correct Answer: x = 7π/6

Solution: 

Solving gives sin(x) = -√3/2, so x = 7π/6 and 11π/6.

Find the solutions of the equation 2sin(x) + √3 = 0.

Practice Questions

Q1
Find the solutions of the equation 2sin(x) + √3 = 0.
  1. x = 5π/6
  2. x = 7π/6
  3. x = π/6
  4. x = 11π/6

Questions & Step-by-Step Solutions

Find the solutions of the equation 2sin(x) + √3 = 0.
Correct Answer: x = 7π/6 and 11π/6
  • 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.
  • Trigonometric Equations – The question tests the ability to solve equations involving trigonometric functions, specifically the sine function.
  • Unit Circle – Understanding the unit circle is essential for identifying angles where the sine function takes specific values.
  • Quadrants of the Unit Circle – Recognizing in which quadrants the sine function is negative is crucial for finding all solutions.
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