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If sin²A + cos²A = 1, what is sin²A when cos A = 0.6?

Practice Questions

Q1
If sin²A + cos²A = 1, what is sin²A when cos A = 0.6?
  1. 0.36
  2. 0.64
  3. 0.76
  4. 0.16

Questions & Step-by-Step Solutions

If sin²A + cos²A = 1, what is sin²A when cos A = 0.6?
  • Step 1: Recall the identity sin²A + cos²A = 1.
  • Step 2: We need to find sin²A when cos A = 0.6.
  • Step 3: First, calculate cos²A by squaring 0.6: (0.6)² = 0.36.
  • Step 4: Substitute cos²A into the identity: sin²A = 1 - cos²A.
  • Step 5: Now, replace cos²A with 0.36: sin²A = 1 - 0.36.
  • Step 6: Perform the subtraction: sin²A = 1 - 0.36 = 0.64.
  • Pythagorean Identity – The relationship sin²A + cos²A = 1 is a fundamental identity in trigonometry that relates the sine and cosine of an angle.
  • Calculating Sine from Cosine – The question tests the ability to derive sin²A from a given value of cos A using the Pythagorean identity.
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