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If cot θ = 3/4, what is the value of sin θ?

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

Options:

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

Correct Answer: 4/5

Solution: 

Using the identity cot θ = cos θ / sin θ, we find sin θ = 4/5.

If cot θ = 3/4, what is the value of sin θ?

Practice Questions

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

Questions & Step-by-Step Solutions

If cot θ = 3/4, what is the value of sin θ?
  • Step 1: Understand that cot θ = 3/4 means that the ratio of cos θ to sin θ is 3/4.
  • Step 2: Write cot θ as cos θ / sin θ, so we have cos θ / sin θ = 3/4.
  • Step 3: Let sin θ = 4k and cos θ = 3k for some value k, since the ratio is 3:4.
  • Step 4: Use the Pythagorean identity sin² θ + cos² θ = 1.
  • Step 5: Substitute sin θ and cos θ into the identity: (4k)² + (3k)² = 1.
  • Step 6: Calculate (16k²) + (9k²) = 1, which simplifies to 25k² = 1.
  • Step 7: Solve for k by dividing both sides by 25: k² = 1/25, so k = 1/5.
  • Step 8: Now find sin θ: sin θ = 4k = 4 * (1/5) = 4/5.
  • Trigonometric Identities – Understanding the relationship between cotangent, sine, and cosine.
  • Pythagorean Theorem – Using the identity sin²θ + cos²θ = 1 to find the values of sine and cosine.
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