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If sin(θ) = 0.8, what is cos(θ) using Pythagorean identity? (2020)

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Question: If sin(θ) = 0.8, what is cos(θ) using Pythagorean identity? (2020)

Options:

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

Correct Answer: 0.6

Solution: 

Using sin²(θ) + cos²(θ) = 1, cos²(θ) = 1 - 0.64 = 0.36, cos(θ) = 0.6

If sin(θ) = 0.8, what is cos(θ) using Pythagorean identity? (2020)

Practice Questions

Q1
If sin(θ) = 0.8, what is cos(θ) using Pythagorean identity? (2020)
  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) using Pythagorean identity? (2020)
  • Step 1: Start with the given value of sin(θ), which is 0.8.
  • Step 2: Use the Pythagorean identity, which states that sin²(θ) + cos²(θ) = 1.
  • Step 3: Calculate sin²(θ) by squaring the value of sin(θ): 0.8 * 0.8 = 0.64.
  • Step 4: Substitute sin²(θ) into the Pythagorean identity: 0.64 + cos²(θ) = 1.
  • Step 5: Rearrange the equation to solve for cos²(θ): cos²(θ) = 1 - 0.64.
  • Step 6: Calculate 1 - 0.64, which equals 0.36.
  • Step 7: Now, take the square root of cos²(θ) to find cos(θ): cos(θ) = √0.36.
  • Step 8: Calculate the square root of 0.36, which is 0.6.
  • Pythagorean Identity – The relationship sin²(θ) + cos²(θ) = 1, which connects sine and cosine values.
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