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Solve the equation sin(2x) = 0 for x in the interval [0, 2π].

Practice Questions

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

Questions & Step-by-Step Solutions

Solve the equation sin(2x) = 0 for x in the interval [0, 2π].
  • Step 1: Start with the equation sin(2x) = 0.
  • Step 2: Recall that the sine function equals zero at integer multiples of π. So, we set 2x = nπ, where n is an integer.
  • Step 3: Solve for x by dividing both sides by 2: x = nπ/2.
  • Step 4: Determine the values of n that keep x within the interval [0, 2π].
  • Step 5: For n = 0, x = 0; for n = 1, x = π/2; for n = 2, x = π; for n = 3, x = 3π/2; for n = 4, x = 2π.
  • Step 6: List the valid solutions: x = 0, π, 2π.
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