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If sin²A + cos²A = 1, what is the value of sin²A when cos A = 0?

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Question: If sin²A + cos²A = 1, what is the value of sin²A when cos A = 0?

Options:

  1. 0
  2. 1
  3. 1/2
  4. Undefined

Correct Answer: 1

Solution: 

If cos A = 0, then sin²A = 1 - cos²A = 1 - 0 = 1.

If sin²A + cos²A = 1, what is the value of sin²A when cos A = 0?

Practice Questions

Q1
If sin²A + cos²A = 1, what is the value of sin²A when cos A = 0?
  1. 0
  2. 1
  3. 1/2
  4. Undefined

Questions & Step-by-Step Solutions

If sin²A + cos²A = 1, what is the value of sin²A when cos A = 0?
  • Step 1: Start with the equation sin²A + cos²A = 1.
  • Step 2: Substitute the value of cos A into the equation. Here, we know cos A = 0.
  • Step 3: Calculate cos²A. Since cos A = 0, then cos²A = 0² = 0.
  • Step 4: Substitute cos²A back into the equation: sin²A + 0 = 1.
  • Step 5: Simplify the equation to find sin²A: sin²A = 1 - 0.
  • Step 6: Therefore, sin²A = 1.
  • Pythagorean Identity – The fundamental trigonometric identity that states sin²A + cos²A = 1.
  • Trigonometric Values – Understanding the values of sine and cosine at specific angles, particularly when cos A = 0.
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