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If sin(θ) = 4/5, what is the value of tan(θ)?

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

Options:

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

Correct Answer: 3/4

Solution: 

Using the identity tan(θ) = sin(θ)/cos(θ) and cos(θ) = √(1 - sin^2(θ)), we find cos(θ) = 3/5. Thus, tan(θ) = (4/5)/(3/5) = 4/3.

If sin(θ) = 4/5, what is the value of tan(θ)?

Practice Questions

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

Questions & Step-by-Step Solutions

If sin(θ) = 4/5, what is the value of tan(θ)?
  • Step 1: We know that sin(θ) = 4/5.
  • Step 2: We need to find cos(θ) using the identity cos(θ) = √(1 - sin^2(θ)).
  • Step 3: First, calculate sin^2(θ): (4/5)² = 16/25.
  • Step 4: Now, substitute sin^2(θ) into the cos(θ) formula: cos(θ) = √(1 - 16/25).
  • Step 5: Simplify inside the square root: 1 - 16/25 = 25/25 - 16/25 = 9/25.
  • Step 6: Now, take the square root: cos(θ) = √(9/25) = 3/5.
  • Step 7: Now we have sin(θ) = 4/5 and cos(θ) = 3/5.
  • Step 8: Use the identity tan(θ) = sin(θ)/cos(θ) to find tan(θ).
  • Step 9: Substitute the values: tan(θ) = (4/5) / (3/5).
  • Step 10: Simplify the fraction: tan(θ) = 4/5 * 5/3 = 4/3.
  • Trigonometric Identities – Understanding and applying the relationship between sine, cosine, and tangent functions.
  • Pythagorean Identity – Using the identity sin²(θ) + cos²(θ) = 1 to find the cosine value from the sine value.
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