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If sin A = 4/5, what is the value of tan A?

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Question: If sin A = 4/5, what is the value of tan A?

Options:

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

Correct Answer: 4/3

Solution: 

Using the identity tan A = sin A / cos A, we find cos A = 3/5, thus tan A = (4/5) / (3/5) = 4/3.

If sin A = 4/5, what is the value of tan A?

Practice Questions

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

Questions & Step-by-Step Solutions

If sin A = 4/5, what is the value of tan A?
  • Step 1: We know that sin A = 4/5.
  • Step 2: We need to find cos A. We can use the Pythagorean identity: sin^2 A + cos^2 A = 1.
  • Step 3: Calculate sin^2 A: (4/5)^2 = 16/25.
  • Step 4: Substitute sin^2 A into the identity: 16/25 + cos^2 A = 1.
  • Step 5: To find cos^2 A, subtract 16/25 from 1: cos^2 A = 1 - 16/25 = 25/25 - 16/25 = 9/25.
  • Step 6: Take the square root of cos^2 A to find cos A: cos A = √(9/25) = 3/5.
  • Step 7: Now we can find tan A using the identity tan A = sin A / cos A.
  • Step 8: Substitute the values: tan A = (4/5) / (3/5).
  • Step 9: Simplify the fraction: tan A = 4/5 * 5/3 = 4/3.
  • Trigonometric Ratios – Understanding the relationships between sine, cosine, and tangent functions.
  • Pythagorean Identity – Using the identity sin²A + cos²A = 1 to find the cosine value from the sine value.
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