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If sin(θ) = 0, what are the possible values of θ?

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Question: If sin(θ) = 0, what are the possible values of θ?

Options:

  1. 0°, 180°
  2. 90°, 270°
  3. 45°, 135°
  4. 30°, 150°

Correct Answer: 0°, 180°

Solution: 

sin(θ) = 0 at θ = 0° and 180°.

If sin(θ) = 0, what are the possible values of θ?

Practice Questions

Q1
If sin(θ) = 0, what are the possible values of θ?
  1. 0°, 180°
  2. 90°, 270°
  3. 45°, 135°
  4. 30°, 150°

Questions & Step-by-Step Solutions

If sin(θ) = 0, what are the possible values of θ?
Correct Answer: 0° and 180°
  • Step 1: Understand that sin(θ) represents the sine of an angle θ.
  • Step 2: Recall that the sine function equals 0 at specific angles.
  • Step 3: Identify the angles where sin(θ) = 0. These angles are 0° and 180°.
  • Step 4: Remember that sine is periodic, meaning it repeats its values. So, sin(θ) = 0 also occurs at 360° and 540°, etc.
  • Step 5: Conclude that the general solutions for sin(θ) = 0 are θ = n * 180°, where n is any integer (0, 1, 2, -1, -2, etc.).
  • Trigonometric Functions – Understanding the sine function and its values at specific angles.
  • Unit Circle – Using the unit circle to determine angles where sine equals zero.
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