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If sin(θ) = 0.8, what is cos(θ)? (2022)

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Question: If sin(θ) = 0.8, what is cos(θ)? (2022)

Options:

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

Correct Answer: 0.6

Solution: 

Using sin²(θ) + cos²(θ) = 1, cos(θ) = √(1 - 0.8²) = √(0.36) = 0.6.

If sin(θ) = 0.8, what is cos(θ)? (2022)

Practice Questions

Q1
If sin(θ) = 0.8, what is cos(θ)? (2022)
  1. 0.6
  2. 0.8
  3. 0.4
  4. 0.2

Questions & Step-by-Step Solutions

If sin(θ) = 0.8, what is cos(θ)? (2022)
  • Step 1: Start with the given information: sin(θ) = 0.8.
  • Step 2: Recall the Pythagorean identity: sin²(θ) + cos²(θ) = 1.
  • Step 3: Calculate sin²(θ): 0.8² = 0.64.
  • Step 4: Substitute sin²(θ) into the identity: 0.64 + cos²(θ) = 1.
  • Step 5: Rearrange the equation to find cos²(θ): cos²(θ) = 1 - 0.64.
  • Step 6: Calculate 1 - 0.64: cos²(θ) = 0.36.
  • Step 7: Take the square root to find cos(θ): cos(θ) = √(0.36).
  • Step 8: Calculate the square root: cos(θ) = 0.6.
  • Pythagorean Identity – The relationship sin²(θ) + cos²(θ) = 1, which relates the sine and cosine of an angle.
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