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If sin(θ) = 3/5, what is cos(θ)?

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Question: If sin(θ) = 3/5, what is cos(θ)?

Options:

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

Correct Answer: 4/5

Solution: 

Using the Pythagorean identity, cos(θ) = √(1 - sin²(θ)) = √(1 - (3/5)²) = 4/5.

If sin(θ) = 3/5, what is cos(θ)?

Practice Questions

Q1
If sin(θ) = 3/5, what is cos(θ)?
  1. 4/5
  2. 3/5
  3. 5/4
  4. 1/5

Questions & Step-by-Step Solutions

If sin(θ) = 3/5, what is cos(θ)?
Correct Answer: 4/5
  • Step 1: Start with the given information: sin(θ) = 3/5.
  • Step 2: Recall the Pythagorean identity, which states that sin²(θ) + cos²(θ) = 1.
  • Step 3: Substitute sin(θ) into the identity: (3/5)² + cos²(θ) = 1.
  • Step 4: Calculate (3/5)²: (3/5)² = 9/25.
  • Step 5: Replace sin²(θ) in the equation: 9/25 + cos²(θ) = 1.
  • Step 6: To isolate cos²(θ), subtract 9/25 from both sides: cos²(θ) = 1 - 9/25.
  • Step 7: Convert 1 to a fraction with a denominator of 25: 1 = 25/25.
  • Step 8: Now, subtract: cos²(θ) = 25/25 - 9/25 = 16/25.
  • Step 9: Take the square root of both sides to find cos(θ): cos(θ) = √(16/25).
  • Step 10: Simplify the square root: cos(θ) = 4/5.
  • Pythagorean Identity – The relationship between sine and cosine, specifically that sin²(θ) + cos²(θ) = 1.
  • Trigonometric Functions – Understanding the values of sine and cosine for angles in a right triangle.
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