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If sin(θ) = 0, what are the possible values of θ in the interval [0, 2π]?

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Question: If sin(θ) = 0, what are the possible values of θ in the interval [0, 2π]?

Options:

  1. 0, π
  2. 0, 2π
  3. π/2, 3π/2
  4. π/4, 3π/4

Correct Answer: 0, π

Solution: 

The angles where sin(θ) = 0 in the interval [0, 2π] are θ = 0 and θ = π.

If sin(θ) = 0, what are the possible values of θ in the interval [0, 2π]?

Practice Questions

Q1
If sin(θ) = 0, what are the possible values of θ in the interval [0, 2π]?
  1. 0, π
  2. 0, 2π
  3. π/2, 3π/2
  4. π/4, 3π/4

Questions & Step-by-Step Solutions

If sin(θ) = 0, what are the possible values of θ in the interval [0, 2π]?
Correct Answer: θ = 0, π
  • Step 1: Understand that sin(θ) = 0 means we are looking for angles where the sine function equals zero.
  • Step 2: Recall that the sine function is zero at specific angles on the unit circle.
  • Step 3: Identify the angles in the interval [0, 2π] where sine is zero. These angles are 0 and π.
  • Step 4: Conclude that the possible values of θ in the interval [0, 2π] are θ = 0 and θ = π.
  • Trigonometric Functions – Understanding the values of sine function and its periodic nature.
  • Unit Circle – Using the unit circle to identify angles corresponding to specific sine values.
  • Interval Notation – Recognizing the specified interval [0, 2π] for the solution.
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