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If sin(α) = 0.6, what is the value of cos(α) using the identity?

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Question: If sin(α) = 0.6, what is the value of cos(α) using the identity?

Options:

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

Correct Answer: 0.8

Solution: 

Using sin^2(α) + cos^2(α) = 1, we find cos(α) = √(1 - 0.6^2) = √(1 - 0.36) = √0.64 = 0.8.

If sin(α) = 0.6, what is the value of cos(α) using the identity?

Practice Questions

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

Questions & Step-by-Step Solutions

If sin(α) = 0.6, what is the value of cos(α) using the identity?
Correct Answer: 0.8
  • Step 1: Start with the given value of sin(α), which is 0.6.
  • Step 2: Use the identity sin^2(α) + cos^2(α) = 1.
  • Step 3: Calculate sin^2(α) by squaring 0.6: 0.6^2 = 0.36.
  • Step 4: Substitute sin^2(α) into the identity: 0.36 + cos^2(α) = 1.
  • Step 5: Rearrange the equation to find cos^2(α): cos^2(α) = 1 - 0.36.
  • Step 6: Calculate 1 - 0.36, which equals 0.64.
  • Step 7: Now, take the square root of 0.64 to find cos(α): cos(α) = √0.64.
  • Step 8: Calculate the square root of 0.64, which is 0.8.
  • Trigonometric Identities – Understanding and applying the Pythagorean identity sin²(α) + cos²(α) = 1 to find the cosine value from the sine value.
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