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If cos B = 5/13, what is the value of sin B?

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Question: If cos B = 5/13, what is the value of sin B?

Options:

  1. 12/13
  2. 5/13
  3. 13/5
  4. 3/5

Correct Answer: 12/13

Solution: 

Using the Pythagorean identity, sin B = √(1 - cos²B) = √(1 - (5/13)²) = √(1 - 25/169) = √(144/169) = 12/13.

If cos B = 5/13, what is the value of sin B?

Practice Questions

Q1
If cos B = 5/13, what is the value of sin B?
  1. 12/13
  2. 5/13
  3. 13/5
  4. 3/5

Questions & Step-by-Step Solutions

If cos B = 5/13, what is the value of sin B?
  • Step 1: Start with the given value of cos B, which is 5/13.
  • Step 2: Use the Pythagorean identity, which states that sin²B + cos²B = 1.
  • Step 3: Substitute the value of cos B into the identity: sin²B + (5/13)² = 1.
  • Step 4: Calculate (5/13)², which is 25/169.
  • Step 5: Rewrite the equation: sin²B + 25/169 = 1.
  • Step 6: To isolate sin²B, subtract 25/169 from both sides: sin²B = 1 - 25/169.
  • Step 7: Convert 1 into a fraction with a denominator of 169: 1 = 169/169.
  • Step 8: Now, subtract: sin²B = 169/169 - 25/169 = 144/169.
  • Step 9: To find sin B, take the square root of both sides: sin B = √(144/169).
  • Step 10: Calculate the square root: sin B = 12/13.
  • Pythagorean Identity – The relationship between sine and cosine, specifically sin²B + cos²B = 1, which allows for the calculation of one function if the other is known.
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