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If sin(θ) = 0.6, what is cos(θ) using the Pythagorean identity?

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Question: If sin(θ) = 0.6, what is cos(θ) using the Pythagorean identity?

Options:

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

Correct Answer: 0.8

Solution: 

Using sin²θ + cos²θ = 1, cos²θ = 1 - 0.6² = 0.64, thus cos(θ) = 0.8.

If sin(θ) = 0.6, what is cos(θ) using the Pythagorean identity?

Practice Questions

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

Questions & Step-by-Step Solutions

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