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Find the solutions of the equation 2sin(x) - 1 = 0.

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Question: Find the solutions of the equation 2sin(x) - 1 = 0.

Options:

  1. π/6
  2. 5Ï€/6
  3. 7Ï€/6
  4. 11Ï€/6

Correct Answer: π/6

Solution: 

The solutions are x = π/6 and x = 5π/6.

Find the solutions of the equation 2sin(x) - 1 = 0.

Practice Questions

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

Questions & Step-by-Step Solutions

Find the solutions of the equation 2sin(x) - 1 = 0.
  • 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 x = Ï€/6 and x = 5Ï€/6.
  • Step 5: Write down the solutions: x = Ï€/6 and x = 5Ï€/6.
  • Trigonometric Equations – The question tests the ability to solve basic trigonometric equations involving the sine function.
  • Unit Circle – Understanding the unit circle is essential for identifying the angles that correspond to specific sine values.
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