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

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

Options:

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

Correct Answer: 12/13

Solution: 

Using the Pythagorean identity, cos A = √(1 - sin²A) = √(1 - (5/13)²) = √(1 - 25/169) = √(144/169) = 12/13.

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

Practice Questions

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

Questions & Step-by-Step Solutions

If sin A = 5/13, what is the value of cos A?
  • Step 1: Start with the given value of sin A, which is 5/13.
  • Step 2: Use the Pythagorean identity, which states that sin²A + cos²A = 1.
  • Step 3: Substitute sin A into the identity: (5/13)² + cos²A = 1.
  • Step 4: Calculate (5/13)², which is 25/169.
  • Step 5: Now the equation looks like this: 25/169 + cos²A = 1.
  • Step 6: To isolate cos²A, subtract 25/169 from both sides: cos²A = 1 - 25/169.
  • Step 7: Convert 1 into a fraction with a denominator of 169: 1 = 169/169.
  • Step 8: Now the equation is: cos²A = 169/169 - 25/169.
  • Step 9: Subtract the fractions: cos²A = (169 - 25)/169 = 144/169.
  • Step 10: To find cos A, take the square root of both sides: cos A = √(144/169).
  • Step 11: Calculate the square root: cos A = 12/13.
  • Pythagorean Identity – The relationship between sine and cosine, specifically that sin²A + cos²A = 1.
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