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What are the solutions of the equation sin(2x) = 0?

Practice Questions

Q1
What are the solutions of the equation sin(2x) = 0?
  1. x = nπ/2
  2. x = nπ
  3. x = nπ + π/2
  4. x = nπ + π

Questions & Step-by-Step Solutions

What are the solutions of the equation sin(2x) = 0?
  • Step 1: Understand the equation sin(2x) = 0. This means we want to find the values of x where the sine of 2x equals zero.
  • Step 2: Recall that the sine function equals zero at integer multiples of π (pi). This means sin(θ) = 0 when θ = nπ, where n is any integer (n ∈ Z).
  • Step 3: Set 2x equal to nπ. So, we write the equation as 2x = nπ.
  • Step 4: Solve for x by dividing both sides of the equation by 2. This gives us x = nπ/2.
  • Step 5: Remember that n can be any integer, so the solutions are x = nπ/2 for n ∈ Z.
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