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If tan(x) = 3/4, what is the value of sin(x)?

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Question: If tan(x) = 3/4, what is the value of sin(x)?

Options:

  1. 3/5
  2. 4/5
  3. 1/5
  4. 0

Correct Answer: 3/5

Solution: 

Using the identity tan(x) = sin(x)/cos(x), we can find sin(x) = 3/5 after calculating the hypotenuse using the Pythagorean theorem.

If tan(x) = 3/4, what is the value of sin(x)?

Practice Questions

Q1
If tan(x) = 3/4, what is the value of sin(x)?
  1. 3/5
  2. 4/5
  3. 1/5
  4. 0

Questions & Step-by-Step Solutions

If tan(x) = 3/4, what is the value of sin(x)?
Correct Answer: 3/5
  • Step 1: Understand that tan(x) = sin(x) / cos(x). We are given that tan(x) = 3/4.
  • Step 2: This means that sin(x) = 3k and cos(x) = 4k for some value k.
  • Step 3: Use the Pythagorean theorem to find the hypotenuse. The formula is sin^2(x) + cos^2(x) = 1.
  • Step 4: Substitute sin(x) and cos(x) into the equation: (3k)^2 + (4k)^2 = 1.
  • Step 5: Simplify the equation: 9k^2 + 16k^2 = 1, which gives 25k^2 = 1.
  • Step 6: Solve for k: k^2 = 1/25, so k = 1/5.
  • Step 7: Now find sin(x): sin(x) = 3k = 3 * (1/5) = 3/5.
  • Trigonometric Identities – Understanding the relationship between sine, cosine, and tangent functions.
  • Pythagorean Theorem – Using the theorem to find the hypotenuse in a right triangle given the lengths of the opposite and adjacent sides.
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