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If sin θ = 0.8, what is the value of cos θ?

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Question: If sin θ = 0.8, what is the value of cos θ?

Options:

  1. 0.6
  2. 0.8
  3. 0.4
  4. 0.2

Correct Answer: 0.6

Solution: 

Using the Pythagorean identity, cos θ = √(1 - sin²θ) = √(1 - 0.8²) = √(1 - 0.64) = √(0.36) = 0.6.

If sin θ = 0.8, what is the value of cos θ?

Practice Questions

Q1
If sin θ = 0.8, what is the value of cos θ?
  1. 0.6
  2. 0.8
  3. 0.4
  4. 0.2

Questions & Step-by-Step Solutions

If sin θ = 0.8, what is the value of cos θ?
  • Step 1: Start with the given value of sin θ, which is 0.8.
  • Step 2: Use the Pythagorean identity, which states that sin²θ + cos²θ = 1.
  • Step 3: Rearrange the identity to find cos²θ: cos²θ = 1 - sin²θ.
  • Step 4: Calculate sin²θ: sin²θ = (0.8)² = 0.64.
  • Step 5: Substitute sin²θ into the equation: cos²θ = 1 - 0.64.
  • Step 6: Calculate 1 - 0.64: cos²θ = 0.36.
  • Step 7: Take the square root of both sides to find cos θ: cos θ = √(0.36).
  • Step 8: Calculate the square root: cos θ = 0.6.
  • Pythagorean Identity – The relationship between sine and cosine, specifically that sin²θ + cos²θ = 1.
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