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If cos(x) = 1/2, what is the value of sin(x)?

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

Options:

  1. √3/2
  2. 1/2
  3. 0
  4. √2/2

Correct Answer: √3/2

Solution: 

Using the identity sin^2(x) + cos^2(x) = 1, we have sin^2(x) = 1 - (1/2)^2 = 1 - 1/4 = 3/4. Therefore, sin(x) = √(3/4) = √3/2.

If cos(x) = 1/2, what is the value of sin(x)?

Practice Questions

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

Questions & Step-by-Step Solutions

If cos(x) = 1/2, what is the value of sin(x)?
Correct Answer: √3/2
  • Step 1: Start with the given information: cos(x) = 1/2.
  • Step 2: Use the Pythagorean identity: sin^2(x) + cos^2(x) = 1.
  • Step 3: Substitute cos(x) into the identity: sin^2(x) + (1/2)^2 = 1.
  • Step 4: Calculate (1/2)^2: (1/2)^2 = 1/4.
  • Step 5: Rewrite the equation: sin^2(x) + 1/4 = 1.
  • Step 6: Subtract 1/4 from both sides: sin^2(x) = 1 - 1/4.
  • Step 7: Calculate 1 - 1/4: 1 - 1/4 = 3/4.
  • Step 8: Now we have sin^2(x) = 3/4.
  • Step 9: Take the square root of both sides: sin(x) = √(3/4).
  • Step 10: Simplify √(3/4): sin(x) = √3/2.
  • Trigonometric Identities – Understanding and applying the Pythagorean identity sin^2(x) + cos^2(x) = 1 to find the value of sin(x) given cos(x).
  • Quadrants of Trigonometric Functions – Recognizing that sin(x) can have both positive and negative values depending on the quadrant in which x lies.
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