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If tan(θ) = 3/4, what is the value of sin(θ)?

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Question: If tan(θ) = 3/4, what is the value of sin(θ)?

Options:

  1. 3/5
  2. 4/5
  3. 5/5
  4. 1

Correct Answer: 3/5

Solution: 

Using the identity sin²(θ) + cos²(θ) = 1, we find sin(θ) = 3/5.

If tan(θ) = 3/4, what is the value of sin(θ)?

Practice Questions

Q1
If tan(θ) = 3/4, what is the value of sin(θ)?
  1. 3/5
  2. 4/5
  3. 5/5
  4. 1

Questions & Step-by-Step Solutions

If tan(θ) = 3/4, what is the value of sin(θ)?
Correct Answer: 3/5
  • Step 1: Understand that tan(θ) = opposite/adjacent. Here, tan(θ) = 3/4 means the opposite side is 3 and the adjacent side is 4.
  • Step 2: Use the Pythagorean theorem to find the hypotenuse. The formula is hypotenuse² = opposite² + adjacent².
  • Step 3: Calculate the hypotenuse: hypotenuse² = 3² + 4² = 9 + 16 = 25.
  • Step 4: Find the hypotenuse by taking the square root: hypotenuse = √25 = 5.
  • Step 5: Now, use the definition of sin(θ) = opposite/hypotenuse. Here, sin(θ) = 3/5.
  • Step 6: Therefore, the value of sin(θ) is 3/5.
  • Trigonometric Identities – Understanding the relationship between sine, cosine, and tangent through the Pythagorean identity.
  • Right Triangle Ratios – Using the definition of tangent as the ratio of opposite to adjacent sides in a right triangle.
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