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If tan θ = 1, what is the value of sin θ?

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Question: If tan θ = 1, what is the value of sin θ?

Options:

  1. 1/√2
  2. 1
  3. 0
  4. √2

Correct Answer: 1/√2

Solution: 

Since tan θ = sin θ / cos θ and tan θ = 1, we have sin θ = cos θ. For θ = 45°, sin θ = 1/√2.

If tan θ = 1, what is the value of sin θ?

Practice Questions

Q1
If tan θ = 1, what is the value of sin θ?
  1. 1/√2
  2. 1
  3. 0
  4. √2

Questions & Step-by-Step Solutions

If tan θ = 1, what is the value of sin θ?
  • Step 1: Understand that tan θ is defined as sin θ divided by cos θ.
  • Step 2: Write the equation for tan θ: tan θ = sin θ / cos θ.
  • Step 3: Since we know tan θ = 1, we can set up the equation: 1 = sin θ / cos θ.
  • Step 4: Rearrange the equation to find that sin θ = cos θ.
  • Step 5: Recognize that sin θ = cos θ at specific angles, one of which is θ = 45°.
  • Step 6: Calculate sin 45° using the known value: sin 45° = 1/√2.
  • Trigonometric Ratios – Understanding the relationship between sine, cosine, and tangent functions.
  • Special Angles – Recognizing the values of sine and cosine for common angles like 45°.
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