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

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

Options:

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

Correct Answer: 12/5

Solution: 

Using the identity tan A = sin A / cos A, we find sin A = √(1 - cos²A) = √(1 - (5/13)²) = 12/13. Thus, tan A = (12/13) / (5/13) = 12/5.

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

Practice Questions

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

Questions & Step-by-Step Solutions

If cos A = 5/13, what is the value of tan A?
  • Step 1: We know that cos A = 5/13.
  • Step 2: We need to find sin A using the identity sin²A + cos²A = 1.
  • Step 3: First, calculate cos²A: (5/13)² = 25/169.
  • Step 4: Now, substitute cos²A into the identity: sin²A + 25/169 = 1.
  • Step 5: To isolate sin²A, subtract 25/169 from both sides: sin²A = 1 - 25/169.
  • Step 6: Convert 1 to a fraction with a denominator of 169: 1 = 169/169.
  • Step 7: Now, subtract: sin²A = 169/169 - 25/169 = 144/169.
  • Step 8: Take the square root of both sides to find sin A: sin A = √(144/169) = 12/13.
  • Step 9: Now we have sin A = 12/13 and cos A = 5/13.
  • Step 10: Use the identity tan A = sin A / cos A: tan A = (12/13) / (5/13).
  • Step 11: Simplify the fraction: tan A = 12/5.
  • Trigonometric Identities – Understanding and applying the relationship between sine, cosine, and tangent functions.
  • Pythagorean Identity – Using the identity sin²A + cos²A = 1 to find the sine value from the cosine value.
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