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If sin C = 0.5, what is the value of cos C?

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Question: If sin C = 0.5, what is the value of cos C?

Options:

  1. √3/2
  2. 1/2
  3. 0.5
  4. √2/2

Correct Answer: √3/2

Solution: 

Using the Pythagorean identity, cos C = √(1 - sin² C) = √(1 - 0.25) = √0.75 = √3/2.

If sin C = 0.5, what is the value of cos C?

Practice Questions

Q1
If sin C = 0.5, what is the value of cos C?
  1. √3/2
  2. 1/2
  3. 0.5
  4. √2/2

Questions & Step-by-Step Solutions

If sin C = 0.5, what is the value of cos C?
  • Step 1: Start with the given value, sin C = 0.5.
  • Step 2: Use the Pythagorean identity, which states that sin² C + cos² C = 1.
  • Step 3: Calculate sin² C by squaring the value of sin C: (0.5)² = 0.25.
  • Step 4: Substitute sin² C into the Pythagorean identity: 0.25 + cos² C = 1.
  • Step 5: Rearrange the equation to find cos² C: cos² C = 1 - 0.25.
  • Step 6: Calculate 1 - 0.25, which equals 0.75.
  • Step 7: Now, take the square root of cos² C to find cos C: cos C = √0.75.
  • Step 8: Simplify √0.75 to √(3/4), which is √3/2.
  • Pythagorean Identity – The relationship between sine and cosine, specifically that sin² C + cos² C = 1.
  • Trigonometric Values – Understanding the specific values of sine and cosine for common angles.
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