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If sin(x) = 3/5, what is the value of cos(x)?

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Question: If sin(x) = 3/5, what is the value of cos(x)?

Options:

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

Correct Answer: 4/5

Solution: 

Using the identity sin^2(x) + cos^2(x) = 1, we have cos^2(x) = 1 - (3/5)^2 = 1 - 9/25 = 16/25. Therefore, cos(x) = ±4/5.

If sin(x) = 3/5, what is the value of cos(x)?

Practice Questions

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

Questions & Step-by-Step Solutions

If sin(x) = 3/5, what is the value of cos(x)?
  • Step 1: Start with the given information: sin(x) = 3/5.
  • Step 2: Recall the Pythagorean identity: sin^2(x) + cos^2(x) = 1.
  • Step 3: Calculate sin^2(x): (3/5)^2 = 9/25.
  • Step 4: Substitute sin^2(x) into the identity: 9/25 + cos^2(x) = 1.
  • Step 5: Rearrange the equation to find cos^2(x): cos^2(x) = 1 - 9/25.
  • Step 6: Convert 1 to a fraction with a denominator of 25: 1 = 25/25.
  • Step 7: Now subtract: cos^2(x) = 25/25 - 9/25 = 16/25.
  • Step 8: Take the square root of both sides to find cos(x): cos(x) = ±√(16/25).
  • Step 9: Simplify the square root: cos(x) = ±4/5.
  • Pythagorean Identity – The relationship between sine and cosine functions, specifically sin^2(x) + cos^2(x) = 1.
  • Quadrants of Trigonometric Functions – Understanding the signs of sine and cosine in different quadrants to determine the correct value of cos(x).
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