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If sin(θ) = 1/√2, what is the value of θ?

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Question: If sin(θ) = 1/√2, what is the value of θ?

Options:

  1. 30°
  2. 45°
  3. 60°
  4. 90°

Correct Answer: 45°

Solution: 

sin(θ) = 1/√2 at θ = 45°.

If sin(θ) = 1/√2, what is the value of θ?

Practice Questions

Q1
If sin(θ) = 1/√2, what is the value of θ?
  1. 30°
  2. 45°
  3. 60°
  4. 90°

Questions & Step-by-Step Solutions

If sin(θ) = 1/√2, what is the value of θ?
Correct Answer: 45°
  • Step 1: Understand that sin(θ) represents the sine of an angle θ.
  • Step 2: Know that sin(θ) = 1/√2 is a common value for sine.
  • Step 3: Recall that the sine function equals 1/√2 at specific angles.
  • Step 4: Recognize that one of those angles is 45° (or π/4 radians).
  • Step 5: Conclude that if sin(θ) = 1/√2, then θ = 45°.
  • Trigonometric Functions – Understanding the values of sine for common angles in the unit circle.
  • Inverse Trigonometric Functions – Using the inverse sine function to find angles corresponding to specific sine values.
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