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

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

Options:

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

Correct Answer: 0.6

Solution: 

Using the Pythagorean identity, cos C = √(1 - sin²C) = √(1 - 0.8²) = √(1 - 0.64) = √(0.36) = 0.6.

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

Practice Questions

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

Questions & Step-by-Step Solutions

If sin C = 0.8, what is the value of cos C?
  • Step 1: Start with the given value, sin C = 0.8.
  • Step 2: Use the Pythagorean identity, which states that sin²C + cos²C = 1.
  • Step 3: Substitute sin C into the identity: 0.8² + cos²C = 1.
  • Step 4: Calculate 0.8², which is 0.64.
  • Step 5: Now the equation looks like this: 0.64 + cos²C = 1.
  • Step 6: To find cos²C, subtract 0.64 from both sides: cos²C = 1 - 0.64.
  • Step 7: Calculate 1 - 0.64, which equals 0.36.
  • Step 8: Now we have cos²C = 0.36.
  • Step 9: To find cos C, take the square root of 0.36: cos C = √0.36.
  • Step 10: Calculate the square root of 0.36, which is 0.6.
  • Pythagorean Identity – The relationship between sine and cosine functions, specifically that sin²C + cos²C = 1.
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