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If tan(θ) = 3/4, what is sin(θ)?

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

Options:

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

Correct Answer: 3/5

Solution: 

Using the identity tan(θ) = sin(θ)/cos(θ), we find sin(θ) = 3/5.

If tan(θ) = 3/4, what is sin(θ)?

Practice Questions

Q1
If tan(θ) = 3/4, what is 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 sin(θ)?
  • Step 1: Understand that tan(θ) = sin(θ) / cos(θ).
  • Step 2: We know tan(θ) = 3/4, so we can write sin(θ) / cos(θ) = 3/4.
  • Step 3: Let sin(θ) = 3k and cos(θ) = 4k for some value k.
  • Step 4: Use the Pythagorean identity: sin²(θ) + cos²(θ) = 1.
  • Step 5: Substitute sin(θ) and cos(θ): (3k)² + (4k)² = 1.
  • Step 6: Simplify: 9k² + 16k² = 1, which gives 25k² = 1.
  • Step 7: Solve for k: k² = 1/25, so k = 1/5.
  • Step 8: Now find sin(θ): sin(θ) = 3k = 3 * (1/5) = 3/5.
  • Trigonometric Identities – Understanding the relationship between sine, cosine, and tangent functions.
  • Pythagorean Theorem in Trigonometry – Using the identity sin²(θ) + cos²(θ) = 1 to find the values of sine and cosine.
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