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If tan θ = 1/√3, what is the value of sin θ?

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Question: If tan θ = 1/√3, what is the value of sin θ?

Options:

  1. 1/2
  2. √3/2
  3. 1/√2
  4. √2/2

Correct Answer: 1/2

Solution: 

Since tan θ = sin θ / cos θ, and tan θ = 1/√3, we can use the 30-60-90 triangle where sin θ = 1/2.

If tan θ = 1/√3, what is the value of sin θ?

Practice Questions

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

Questions & Step-by-Step Solutions

If tan θ = 1/√3, what is the value of sin θ?
  • Step 1: Understand that tan θ is the ratio of sin θ to cos θ.
  • Step 2: Write the equation: tan θ = sin θ / cos θ.
  • Step 3: Since tan θ = 1/√3, we can set up the equation: sin θ / cos θ = 1/√3.
  • Step 4: Recognize that in a 30-60-90 triangle, the sides are in the ratio 1:√3:2.
  • Step 5: In this triangle, the angle opposite the side of length 1 (the shortest side) is 30 degrees.
  • Step 6: For θ = 30 degrees, sin θ = opposite/hypotenuse = 1/2.
  • Step 7: Therefore, the value of sin θ is 1/2.
  • Trigonometric Ratios – Understanding the relationship between sine, cosine, and tangent functions.
  • Special Triangles – Utilizing the properties of 30-60-90 triangles to find trigonometric values.
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