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Solve the equation 3sin(x) - 4 = 0 for x in the interval [0, 2Ï€].

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What’s inside this PDF?

Question: Solve the equation 3sin(x) - 4 = 0 for x in the interval [0, 2Ï€].

Options:

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

Correct Answer: π/3

Solution: 

The solution is x = π/3.

Solve the equation 3sin(x) - 4 = 0 for x in the interval [0, 2Ï€].

Practice Questions

Q1
Solve the equation 3sin(x) - 4 = 0 for x in the interval [0, 2Ï€].
  1. π/6
  2. π/3
  3. 2Ï€/3
  4. 5Ï€/6

Questions & Step-by-Step Solutions

Solve the equation 3sin(x) - 4 = 0 for x in the interval [0, 2Ï€].
  • Step 1: Start with the equation 3sin(x) - 4 = 0.
  • Step 2: Add 4 to both sides of the equation to isolate the sine term: 3sin(x) = 4.
  • Step 3: Divide both sides by 3 to solve for sin(x): sin(x) = 4/3.
  • Step 4: Notice that sin(x) cannot be greater than 1. Since 4/3 is greater than 1, there are no solutions for x in the interval [0, 2Ï€].
  • Trigonometric Equations – The question tests the ability to solve a basic trigonometric equation involving the sine function.
  • Interval Restrictions – The solution must be found within a specified interval, which is [0, 2Ï€] in this case.
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