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If sin(x) = 1/√2, what is cos(x)?

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Question: If sin(x) = 1/√2, what is cos(x)?

Options:

  1. 1/√2
  2. 0
  3. √2/2
  4. 1

Correct Answer: 1/√2

Solution: 

Using the identity sin^2(x) + cos^2(x) = 1, we have cos^2(x) = 1 - (1/√2)^2 = 1 - 1/2 = 1/2. Thus, cos(x) = ±1/√2.

If sin(x) = 1/√2, what is cos(x)?

Practice Questions

Q1
If sin(x) = 1/√2, what is cos(x)?
  1. 1/√2
  2. 0
  3. √2/2
  4. 1

Questions & Step-by-Step Solutions

If sin(x) = 1/√2, what is cos(x)?
  • Step 1: Start with the given equation: sin(x) = 1/√2.
  • Step 2: Recall the Pythagorean identity: sin^2(x) + cos^2(x) = 1.
  • Step 3: Calculate sin^2(x): (1/√2)^2 = 1/2.
  • Step 4: Substitute sin^2(x) into the identity: 1/2 + cos^2(x) = 1.
  • Step 5: Rearrange the equation to find cos^2(x): cos^2(x) = 1 - 1/2.
  • Step 6: Simplify the right side: cos^2(x) = 1/2.
  • Step 7: Take the square root of both sides to find cos(x): cos(x) = ±√(1/2).
  • Step 8: Simplify √(1/2) to get cos(x) = ±1/√2.
  • Trigonometric Identities – Understanding and applying the Pythagorean identity sin^2(x) + cos^2(x) = 1 to find the cosine value from a given sine value.
  • Quadrants of Trigonometric Functions – Recognizing that the cosine function can be positive or negative depending on the angle's quadrant.
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